Shortcuts of Freely Relaxing Systems Using Equilibrium Physical Observables.

Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.

Multifractality in spin glasses.

We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Finite-size scaling of the random-field Ising model above the upper critical dimension.

Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of statistical physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension D=7, i.e., above its upper critical dimension D_{u}=6, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions D>D_{u}, linear length scale L should be replaced in finite-size scaling expressions by the effective scale L_{eff}=L^{D/D_{u}}. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.

Genetic analysis of resistance to bean leaf crumple virus identifies a candidate LRR-RLK gene.

Bean leaf crumple virus (BLCrV) is a novel begomovirus (family Geminiviridae, genus Begomovirus) infecting common bean (Phaseolus vulgaris L.), threatening bean production in Latin America. Genetic resistance is required to ensure yield stability and reduce the use of insecticides, yet the available resistance sources are limited. In this study, three common bean populations containing a total of 558 genotypes were evaluated in different yield and BLCrV resistance trials under natural infection in the field. A genome-wide association study identified the locus BLC7.1 on chromosome Pv07 at 3.31 Mbp, explaining 8 to 16% of the phenotypic variation for BLCrV resistance. In comparison, whole-genome regression models explained 51 to 78% of the variation and identified the same region on Pv07 to confer resistance. The most significantly associated markers were located within the gene model Phvul.007G040400, which encodes a leucine-rich repeat receptor-like kinase subfamily III member and is likely to be involved in the innate immune response against the virus. The allelic diversity within this gene revealed five different haplotype groups, one of which was significantly associated with BLCrV resistance. As the same genome region was previously reported to be associated with resistance against other geminiviruses affecting common bean, our study highlights the role of previous breeding efforts for virus resistance in the accumulation of positive alleles against newly emerging viruses. In addition, we provide novel diagnostic single-nucleotide polymorphism markers for marker-assisted selection to exploit BLC7.1 for breeding against geminivirus diseases in one of the most important food crops worldwide.

Slow growth of magnetic domains helps fast evolution routes for out-of-equilibrium dynamics.

Cooling and heating faster a system is a crucial problem in science, technology, and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is not a trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely, the two-dimensional Ising model.

Genetic mapping for agronomic traits in a MAGIC population of common bean (Phaseolus vulgaris L.) under drought conditions.

BACKGROUND: Common bean is an important staple crop in the tropics of Africa, Asia and the Americas. Particularly smallholder farmers rely on bean as a source for calories, protein and micronutrients. Drought is a major production constraint for common bean, a situation that will be aggravated with current climate change scenarios. In this context, new tools designed to understand the genetic basis governing the phenotypic responses to abiotic stress are required to improve transfer of desirable traits into cultivated beans. RESULTS: A multiparent advanced generation intercross (MAGIC) population of common bean was generated from eight Mesoamerican breeding lines representing the phenotypic and genotypic diversity of the CIAT Mesoamerican breeding program. This population was assessed under drought conditions in two field trials for yield, 100 seed weight, iron and zinc accumulation, phenology and pod harvest index. Transgressive segregation was observed for most of these traits. Yield was positively correlated with yield components and pod harvest index (PHI), and negative correlations were found with phenology traits and micromineral contents. Founder haplotypes in the population were identified using Genotyping by Sequencing (GBS). No major population structure was observed in the population. Whole Genome Sequencing (WGS) data from the founder lines was used to impute genotyping data for GWAS. Genetic mapping was carried out with two methods, using association mapping with GWAS, and linkage mapping with haplotype-based interval screening. Thirteen high confidence QTL were identified using both methods and several QTL hotspots were found controlling multiple traits. A major QTL hotspot located on chromosome Pv01 for phenology traits and yield was identified. Further hotspots affecting several traits were observed on chromosomes Pv03 and Pv08. A major QTL for seed Fe content was contributed by MIB778, the founder line with highest micromineral accumulation. Based on imputed WGS data, candidate genes are reported for the identified major QTL, and sequence changes were identified that could cause the phenotypic variation. CONCLUSIONS: This work demonstrates the importance of this common bean MAGIC population for genetic mapping of agronomic traits, to identify trait associations for molecular breeding tool design and as a new genetic resource for the bean research community.

Genomic Prediction of Agronomic Traits in Common Bean (Phaseolus vulgaris L.) Under Environmental Stress.

In plant and animal breeding, genomic prediction models are established to select new lines based on genomic data, without the need for laborious phenotyping. Prediction models can be trained on recent or historic phenotypic data and increasingly available genotypic data. This enables the adoption of genomic selection also in under-used legume crops such as common bean. Beans are an important staple food in the tropics and mainly grown by smallholders under limiting environmental conditions such as drought or low soil fertility. Therefore, genotype-by-environment interactions (G × E) are an important consideration when developing new bean varieties. However, G × E are often not considered in genomic prediction models nor are these models implemented in current bean breeding programs. Here we show the prediction abilities of four agronomic traits in common bean under various environmental stresses based on twelve field trials. The dataset includes 481 elite breeding lines characterized by 5,820 SNP markers. Prediction abilities over all twelve trials ranged between 0.6 and 0.8 for yield and days to maturity, respectively, predicting new lines into new seasons. In all four evaluated traits, the prediction abilities reached about 50-80% of the maximum accuracies given by phenotypic correlations and heritability. Predictions under drought and low phosphorus stress were up to 10 and 20% improved when G × E were included in the model, respectively. Our results demonstrate the potential of genomic selection to increase the genetic gain in common bean breeding. Prediction abilities improved when more phenotypic data was available and G × E could be accounted for. Furthermore, the developed models allowed us to predict genotypic performance under different environmental stresses. This will be a key factor in the development of common bean varieties adapted to future challenging conditions.

Evidence for Supersymmetry in the Random-Field Ising Model at D=5.

We provide a nontrivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check these relationships in a finite-size scaling calculation and then perform a high-accuracy test. While the supersymmetric predictions are satisfied even to our high accuracy at D=5, they fail to describe our results at D=4.

The Mpemba effect in spin glasses is a persistent memory effect.

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom-built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a nonequilibrium process, governed by the coherence length ξ of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and ξ that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.

Fine-mapping of angular leaf spot resistance gene Phg-2 in common bean and development of molecular breeding tools.

KEY MESSAGE: The Common Bean Angular Leaf Spot Resistance Gene Phg-2 was fine-mapped to a 409-Kbp region, and molecular markers for breeders were developed and validated in field experiments. Common bean (Phaseolus vulgaris L.) is an important food legume in Latin America, Asia and Africa. It is an important source of protein, carbohydrates and micro-minerals, particularly for smallholder farmers. Common bean productivity is affected by angular leaf spot (ALS) disease caused by the pathogenic fungus Pseudocercospora griseola, resulting in significant yield losses, particularly in low-input smallholder farming systems in the tropics. The ALS resistance gene Phg-2, which was found in several highly resistant common bean genotypes, was investigated in crosses between Mesoamerican pre-breeding lines and elite Andean breeding lines. Next-generation sequencing (NGS) data sets were used to design new SNP-based molecular markers. The Phg-2 locus was confirmed to be the major locus providing ALS resistance in these crosses. The locus was fine-mapped to a 409-Kbp region on chromosome 8. Two clusters of highly related LRR genes were identified in this region, which are the best candidate genes for Phg-2. Molecular markers were identified that are closely linked to the Phg-2 resistance gene and also highly specific to the donor germplasm. Marker-assisted selection (MAS) was used to introgress the Phg-2 resistance locus into Andean breeding germplasm using MAB lines. The usefulness of molecular markers in MAS was confirmed in several field evaluations in complex breeding crosses, under inoculation with different ALS pathotypes. This project demonstrates that NGS data are a powerful tool for the characterization of genetic loci and can be applied in the development of breeding tools.

An Ising model for metal-organic frameworks.

We present a three-dimensional Ising model where lines of equal spins are frozen such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH4) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.

Temperature Scaling Law for Quantum Annealing Optimizers.

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Advantages of Unfair Quantum Ground-State Sampling.

The debate around the potential superiority of quantum annealers over their classical counterparts has been ongoing since the inception of the field. Recent technological breakthroughs, which have led to the manufacture of experimental prototypes of quantum annealing optimizers with sizes approaching the practical regime, have reignited this discussion. However, the demonstration of quantum annealing speedups remains to this day an elusive albeit coveted goal. We examine the power of quantum annealers to provide a different type of quantum enhancement of practical relevance, namely, their ability to serve as useful samplers from the ground-state manifolds of combinatorial optimization problems. We study, both numerically by simulating stoquastic and non-stoquastic quantum annealing processes, and experimentally, using a prototypical quantum annealing processor, the ability of quantum annealers to sample the ground-states of spin glasses differently than thermal samplers. We demonstrate that (i) quantum annealers sample the ground-state manifolds of spin glasses very differently than thermal optimizers (ii) the nature of the quantum fluctuations driving the annealing process has a decisive effect on the final distribution, and (iii) the experimental quantum annealer samples ground-state manifolds significantly differently than thermal and ideal quantum annealers. We illustrate how quantum annealers may serve as powerful tools when complementing standard sampling algorithms.

A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements.

We have performed a very accurate computation of the nonequilibrium fluctuation-dissipation ratio for the 3D Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions.

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions.

By performing a high-statistics simulation of the D=4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

Unraveling Quantum Annealers using Classical Hardness.

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as 'D-Wave' chips, promise to solve practical optimization problems potentially faster than conventional 'classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize 'temperature chaos' as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

Universality in the three-dimensional random-field Ising model.

We solve a long-standing puzzle in statistical mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.

Thermodynamic glass transition in a spin glass without time-reversal symmetry.

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.