[en] An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst--van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort

[en] We propose a new propagation algorithm for the minimization of the Bethe free energy for a generic lattice model with pair interactions. The algorithm turns out to be more stable than belief propagation, as it reaches a fixed point also for highly frustrated systems such as spin glasses, and faster than the provably convergent double loop algorithms

[en] In a cellular environment, confinement and macromolecular crowding play an important role in thermal stability and folding kinetics of a protein. We have resorted to a generalized version of the Wako–Saitô–Muñoz–Eaton model for protein folding to study the behavior of six different protein structures confined between two walls. Changing the distance 2R between the walls, we found, in accordance with previous studies, two confinement regimes: starting from large R and decreasing R, confinement first enhances the stability of the folded state as long as this is compact and until a given value of R; then a further decrease of R leads to a decrease of folding temperature and folding rate. We found that in the low confinement regime, both unfolding temperatures and logarithm of folding rates scale as R"−"γ where γ values lie in between 1.42 and 2.35

[en] We use the cluster variation method (CVM) and Monte Carlo simulations to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. This model corresponds to the usual three-dimensional cubic Ising model with nearest, next to the nearest, and plaquette interactions in the region with degenerate lamellar ground states. The picture of the phase diagram given by the CVM is in good agreement with the results of Monte Carlo simulations, and it is shown that the gonihedric model is in the same universality class of the ordinary three-dimensional Ising model. (orig.)

[en] We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by means of bounds, becoming tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones in the symmetric case of equal binding/unbinding rates. The theory predicts that a dynamical transition will occur in this case as well. (paper)

[en] In a previous study we developed a mean-field theory of dynamical transitions for the totally-asymmetric simple-exclusion process with open boundaries and Langmuir kinetics, in the so-called balanced regime, characterized by equal binding and unbinding rates. Here we show that simply including the possibility of unbalanced rates gives rise to an unexpectedly richer dynamical phase diagram. In particular, the current work predicts an unusual type of dynamical transition, which exhibits certain similarities with first-order phase transitions of equilibrium systems. We also point out that different types of dynamical transition are accompanied by different structural changes in the (mean-field) relaxation spectrum. (paper)

[en] We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view of various (previously known) approximation schemes, and suggests quite a systematic way to improve the level of accuracy. We compare the different approximations with Monte Carlo simulations on a reversible (susceptible-infected-susceptible) discrete-time epidemic-spreading model on random graphs. (paper: interdisciplinary statistical mechanics)

[en] We use the Bethe–Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available. (paper)

[en] Fluctuation relations for the entropy production in non-equilibrium stationary states of Ising models are investigated by means of Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external driving will be studied. In the first case, considering different kinetic rules and couplings with the baths, the behaviors of the probability distributions of the heat exchanged in time τ with the thermostats, both in the disordered phase and in the low temperature phase, are discussed. The fluctuation relation is always followed in the large τ limit and deviations from linear response theory are observed. Finite τ corrections are shown to obey a scaling behavior. In the other case the system is in contact with a single heat bath, but work is done by shearing it. Also for this system, using the statistics collected for the mechanical work we show the validity of the fluctuation relation and the preasymptotic corrections behave analogously to those for the case with two baths