Related papers: A universal form of slow dynamics in zero-temperat…
We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly…
We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a…
We have revisited the non-conserved (or model A) critical dynamics of the two-dimensional Ising model through numerical simulations of its lattice and continuum formulations --Glauber dynamics and the timedependent Ginzburg-Landau (TDGL)…
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field…
The front dynamics in the Harper (or Aubry-Andr\'e) model (which has a localization transition) is investigated using two different settings, particle number front where the system is at zero temperature, and initially, the particle numbers…
Perturbation theory for the random-field Ising model (RFIM) has the infamous attribute that it predicts at all orders a dimensional-reduction property for the critical behavior that turns out to be wrong in low dimension. Guided by our…
The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question…
By utilizing the effective-field theory based on the Glauber-type stochastic dynamics, the dynamic behaviors of the hexagonal Ising nanowire (HIN) system in the presence of a time dependent magnetic field are obtained. The time variations…
We study the Glauber dynamics for the zero-temperature Ising model in dimension d=4 with "plus" boundary condition.Let T+ be the time needed for an hypercube of size L entirely filled with "minus" spins to become entirely "plus". We prove…
Adaptive Langevin dynamics is a method for sampling the Boltzmann-Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. The method replaces the…
We consider a one-dimensional Ising model each of whose $N$ spins is in contact with two thermostats of distinct temperatures $T_1$ and $T_2$. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an…
We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world…
We derive stationary measures for certain zero-temperature random polymer models, which we believe are new in the case of the zero-temperature limit of the beta random polymer (that has been called the river delta model). To do this, we…
This paper provides an overview of the research on the metastable behavior of the Ising model. We analyze the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that…
We consider a one-dimensional microscopic reaction-diffusion process obtained as a superposition of a Glauber and a Kawasaki dynamics. The reaction term is tuned so that a dynamical phase transition occurs in the model as a suitable…
We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories. In this approach trajectories are classified according to a dynamical…
Quantum Ising model is an exactly solvable model of quantum phase transition. This paper gives an exact solution when the system is driven through the critical point at finite rate. The evolution goes through a series of Landau-Zener level…
We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the…
A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for…
Hysteresis is observed at second order phase transitions. Universal scaling formul\ae{} for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical…