Dimer Coupling Energies of the Si(001) Surface.

The coupling energies between the buckled dimers of the Si(001) surface were determined through analysis of the anisotropic critical behavior of its order-disorder phase transition. Spot profiles in high-resolution low-energy electron diffraction as a function of temperature were analyzed within the framework of the anisotropic two-dimensional Ising model. The validity of this approach is justified by the large ratio of correlation lengths, ξ_{∥}^{+}/ξ_{⊥}^{+}=5.2 of the fluctuating c(4×2) domains above the critical temperature T_{c}=(190.6±10) K. We obtain effective couplings J_{∥}=(-24.9±1.3) meV along the dimer rows and J_{⊥}=(-0.8±0.1) meV across the dimer rows, i.e., antiferromagneticlike coupling of the dimers with c(4×2) symmetry.

Many-body critical Casimir interactions in colloidal suspensions.

We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z(2) symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.

Comment on "Casimir force in the O(n→∞) model with free boundary conditions".

In a recent paper by D. Dantchev, J. Bergknoff, and J. Rudnick [Phys. Rev. E 89, 042116 (2014)], the problem of the Casimir force in the O(n) model on a slab with free boundary conditions, investigated earlier by us [Europhys. Lett. 100, 10004 (2012)], is reconsidered using a mean-spherical model with separate constraints for each layer. The authors (i) question the applicability of the Ginzburg-Landau-Wilson approach to the low-temperature regime, arguing for the superiority of their model compared to the family of ϕ(4) models A and B whose numerically exact solutions we determined both for values of the coupling constant 0

Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: isotropic case.

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.

Large-n approach to thermodynamic Casimir effects in slabs with free surfaces.

The classical n-vector ϕ{4} model with O(n) symmetrical Hamiltonian H is considered in a ∞{2}×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature T_{c}. Their n=∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L{-1}, anomalous ones ∝L{-1}lnL should occur. They can be considerably decreased by taking an appropriate g→∞ (T_{c}→∞) limit of the ϕ{4} interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness L_{eff}=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of {4}He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below T_{c}. The results are in conformity with various analytically known exact properties of the scaling functions.

Strongly anisotropic nonequilibrium phase transition in Ising models with friction.

The nonequilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced friction near the critical point. We first consider high driving velocities and demonstrate that both systems are in the same universality class and undergo a strongly anisotropic nonequilibrium phase transition, with anisotropy exponent θ=3. Within a field theoretical ansatz the simulation results are confirmed. The crossover from Ising to mean field behavior in dependency of system size and driving velocity is analyzed using crossover scaling. It turns out that for all finite velocities the phase transition becomes strongly anisotropic in the thermodynamic limit.

Aspect-ratio dependence of thermodynamic Casimir forces.

We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature T(c). Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary ρ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for ρ=1 and becomes repulsive in periodic systems for ρ>1.

Nonequilibrium phase transition in an exactly solvable driven Ising model with friction.

A driven Ising model with friction due to magnetic correlations was proposed by Kadau [Phys. Rev. Lett. 101, 137205 (2008)]. The nonequilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations. In the limit of high driving velocities v the model shows mean-field behavior due to dimensional reduction and can be solved exactly for various geometries. The simulations are performed with three different single spin-flip rates: the common Metropolis and Glauber rates as well as a multiplicative rate. Due to the nonequilibrium nature of the model all rates lead to different critical temperatures at v>0, while the exact solution matches the multiplicative rate. Finally, the crossover from Ising to mean-field behavior as function of velocity and system size is analyzed in one and two dimensions.

Magnetic friction in Ising spin systems.

A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. A surprising effect is observed in the ferromagnetically ordered phase: The relative motion can act like a heat pump cooling the spins in the vicinity of the friction surface.

Thermodynamic Casimir effect in 4He films near Tlambda: Monte Carlo results.

The universal finite-size scaling function of the critical Casimir force for the three dimensional XY universality class with Dirichlet boundary conditions is determined using Monte Carlo simulations. The results are in excellent agreement with recent experiments on 4He Films at the superfluid transition and with available theoretical predictions.

Shellwise Mackay transformation in iron nanoclusters.

Structure and magnetism of iron clusters with up to 641 atoms have been investigated by means of density functional theory calculations including full geometric optimizations. Body-centered cubic (bcc) isomers are found to be lowest in energy when the clusters contain more than about 100 atoms. In addition, another stable conformation has been identified for magic-number clusters, which lies well within the range of thermal energies as compared to the bcc isomers. Its structure is characterized by a close-packed particle core and an icosahedral surface, while intermediate shells are partially transformed along the Mackay path between icosahedral and cuboctahedral geometry. The gradual transformation results in a favorable bcc environment for the subsurface atoms. For Fe55, the shellwise Mackay-transformed morphology is a promising candidate for the ground state.