Communication: Weakening the critical dynamical slowing down of models with SALR interactions.

In systems with frustration, the critical slowing down of the dynamics severely impedes the numerical study of phase transitions for even the simplest of lattice models. In order to help sidestep the gelation-like sluggishness, a clearer understanding of the underlying physics is needed. Here, we first obtain generic insight into that phenomenon by studying one-dimensional and Bethe lattice versions of a schematic frustrated model, the axial next-nearest neighbor Ising (ANNNI) model. Based on these findings, we formulate two cluster algorithms that speed up the simulations of the ANNNI model on a 2D square lattice. Although these schemes do not eliminate the critical slowing own, speed-ups of factors up to 40 are achieved in some regimes.

Crisis propagation in a heterogeneous self-reflexive DSGE model.

We study a self-reflexive DSGE model with heterogeneous households, aimed at characterising the impact of economic recessions on the different strata of the society. Our framework allows to analyse the combined effect of income inequalities and confidence feedback mediated by heterogeneous social networks. By varying the parameters of the model, we find different crisis typologies: loss of confidence may propagate mostly within high income households, or mostly within low income households, with a rather sharp transition between the two. We find that crises are more severe for segregated networks (where confidence feedback is essentially mediated between agents of the same social class), for which cascading contagion effects are stronger. For the same reason, larger income inequalities tend to reduce, in our model, the probability of global crises. Finally, we are able to reproduce a perhaps counter-intuitive empirical finding: in countries with higher Gini coefficients, the consumption of the lowest income households tends to drop less than that of the highest incomes in crisis times.

Solution of disordered microphases in the Bethe approximation.

The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.

V-, U-, L- or W-shaped economic recovery after Covid-19: Insights from an Agent Based Model.

We discuss the impact of a Covid-19-like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state. We then discuss two policies that attempt to moderate the impact of the shock: giving easy credit to firms, and the so-called helicopter money, i.e. injecting new money into the households savings. We find that both policies are effective if strong enough. We highlight the potential danger of terminating these policies too early, although inflation is substantially increased by lax access to credit. Finally, we consider the impact of a second lockdown. While we only discuss a limited number of scenarios, our model is flexible and versatile enough to accommodate a wide variety of situations, thus serving as a useful exploratory tool for a qualitative, scenario-based understanding of post-Covid recovery. The corresponding code is available on-line.

CDK-Regulated Phase Separation Seeded by Histone Genes Ensures Precise Growth and Function of Histone Locus Bodies.

Many membraneless organelles form through liquid-liquid phase separation, but how their size is controlled and whether size is linked to function remain poorly understood. The histone locus body (HLB) is an evolutionarily conserved nuclear body that regulates the transcription and processing of histone mRNAs. Here, we show that Drosophila HLBs form through phase separation. During embryogenesis, the size of HLBs is controlled in a precise and dynamic manner that is dependent on the cell cycle and zygotic histone gene activation. Control of HLB growth is achieved by a mechanism integrating nascent mRNAs at the histone locus, which facilitates phase separation, and the nuclear concentration of the scaffold protein multi-sex combs (Mxc), which is controlled by the activity of cyclin-dependent kinases. Reduced Cdk2 activity results in smaller HLBs and the appearance of nascent, misprocessed histone mRNAs. Thus, our experiments identify a mechanism linking nuclear body growth and size with gene expression.

Velocity and Speed Correlations in Hamiltonian Flocks.

We study a 2D Hamiltonian fluid made of particles carrying spins coupled to their velocities. At low temperatures and intermediate densities, this conservative system exhibits phase coexistence between a collectively moving droplet and a still gas. The particle displacements within the droplet have remarkably similar correlations to those of birds flocks. The center of mass behaves as an effective self-propelled particle, driven by the droplet's total magnetization. The conservation of a generalized angular momentum leads to rigid rotations, opposite to the fluctuations of the magnetization orientation that, however small, are responsible for the shape and scaling of the correlations.

Confidence collapse in a multihousehold, self-reflexive DSGE model.

We investigate a multihousehold dynamic stochastic general equilibrium (DSGE) model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short-lived recessions; and alternation of high- and low-output states where a relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, narratives become an important monetary policy tool that can help steer the economy back on track.

Ferromagnetism-induced phase separation in a two-dimensional spin fluid.

We study the liquid-gas phase separation observed in a system of repulsive particles dressed with ferromagnetically aligning spins, a so-called "spin fluid." Microcanonical ensemble numerical simulations of finite-size systems reveal that magnetization sets in and induces a liquid-gas phase separation between a disordered gas and a ferromagnetic dense phase at low enough energies and large enough densities. The dynamics after a quench into the coexistence region show that the order parameter associated with the liquid-vapor phase separation follows an algebraic law with an unusual exponent, as it is forced to synchronize with the growth of the magnetization: this suggests that for finite size systems the magnetization sets in along a Curie line, which is also the gas-side spinodal line, and that the coexistence region ends at a tricritical point. This picture is confirmed at the mean-field level with different approximation schemes, namely, a Bethe lattice resolution and a virial expansion complemented by the introduction of a self-consistent Weiss-like molecular field. However, a detailed finite-size scaling analysis shows that in two dimensions the ferromagnetic phase escapes the Berezinskii-Kosterlitz-Thouless scenario and that the long-range order is not destroyed by the unbinding of topological defects. The Curie line thus becomes a magnetic crossover in the thermodynamic limit. Finally, the effects of the magnetic interaction range and those of the interaction softness are characterized within a mean-field semianalytical low-density approach.

Spontaneous instabilities and stick-slip motion in a generalized Hébraud-Lequeux model.

We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.

Endogenous crisis waves: stochastic model with synchronized collective behavior.

We propose a simple framework to understand commonly observed crisis waves in macroeconomic agent-based models, which is also relevant to a variety of other physical or biological situations where synchronization occurs. We compute exactly the phase diagram of the model and the location of the synchronization transition in parameter space. Many modifications and extensions can be studied, confirming that the synchronization transition is extremely robust against various sources of noise or imperfections.

Random-field-like criticality in glass-forming liquids.

We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration. We discuss to what extent this field-theoretical description and the mapping to the random field Ising model hold in the whole supercooled liquid regime, in particular, near the glass transition.

Thermal phase transitions in artificial spin ice.

We use the sixteen-vertex model to describe bidimensional artificial spin ice. We find excellent agreement between vertex densities in 15 differently grown samples and the predictions of the model. Our results demonstrate that the samples are in usual thermal equilibrium away from a critical point separating a disordered and an antiferromagnetic phase in the model. The second-order phase transition that we predict suggests that the spatial arrangement of vertices in near-critical artificial spin ice should be studied in more detail in order to verify whether they show the expected space and time long-range correlations.

Renormalization group analysis of the random first-order transition.

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in the mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.

Anomalous nonlinear response of glassy liquids: general arguments and a mode-coupling approach.

We study theoretically the nonlinear response properties of glass formers. We establish several general results, which together with the assumption of time-temperature superposition, lead to a relation between the nonlinear response and the derivative of the linear response with respect to temperature. Using results from mode-coupling theory and scaling arguments valid close to the glass transition, we obtain the frequency and temperature dependence of the nonlinear response in the alpha- and beta-regimes. Our results demonstrate that supercooled liquids are characterized by responses to external perturbations that become increasingly nonlinear as the glass transition is approached. These results are extended to the case of inhomogeneous perturbing fields.

Bose-Einstein condensation in quantum glasses.

The role of geometrical frustration in strongly interacting bosonic systems is studied with a combined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behavior. The differences between such a phase and the otherwise insulating "Bose glasses" are elucidated.

Lattice model for colloidal gels and glasses.

We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied, it reproduces many characteristic phenomena of liquids, glasses, and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the re-entrance of the glass transition.

Statistical mechanics of the hitting set problem.

In this paper we present a detailed study of the hitting set (HS) problem. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the group testing procedures where one wants to detect defective items in a large group by pool testing. Using a statistical mechanics approach based on the cavity method, we study the phase diagram of the HS problem, in the case of random regular hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HS problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hitting set problem.

Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids.

In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.

Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion.

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.

Granular species segregation under vertical tapping: effects of size, density, friction, and shaking amplitude.

We present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive "segregation diagram" and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.