Related papers: Glauber dynamics on trees:Boundary conditions and …
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law''…
In this paper we consider the Glauber dynamics for a disordered ferromagnetic Ising model, in the region of phase coexistence. It was conjectured several decades ago that the spin autocorrelation decays as a negative power of time [Huse and…
This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…
The Ising model doesn't have a strictly defined dynamics, only a spectrum. There are different ways to equip it with a time dependence e.g. the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master…
The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…
We analyse the metastable behaviour of the dilute Curie-Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are Bernoulli random variables with mean $p\in…
Meta-stable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a…
The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial…
We consider the Glauber dynamics for model of polymer interacting with a substrate or wall. The state space is the set of one-dimensional nearest-neighbor paths on $\mathbb{Z}$ with nonnegative integer coordinates, starting at $0$ and…
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter dynamic, and a coalescing particle model. In each of the…
We study the dynamic phase transition properties for the mixed spin-(1/2, 1) Ising model on a square lattice under a time-dependent magnetic field by means the effective-field theory (EFT) based on the Glauber dynamics. We present the…
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…
We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of…
In this paper, we explore the metastable behavior of the Glauber dynamics associated with the three-state Potts model with an asymmetrical external field at a low-temperature regime. The model exhibits three monochromatic configurations: a…
We study Glauber dynamics for the low temperature $(2+1)$D Solid-On-Solid model on a box of side-length $n$ with a floor at height $0$ (inducing entropic repulsion) and a competing bulk external field $\lambda$ pointing down (the prewetting…
We study Swendsen--Wang dynamics for the critical $q$-state Potts model on the square lattice. For $q=2,3,4$, where the phase transition is continuous, the mixing time $t_{\textrm{mix}}$ is expected to obey a universal power-law independent…
Multiscale metrics such as negative Sobolev norms are effective for quantifying the degree of mixedness of a passive scalar field advected by an incompressible flow in the absence of diffusion. In this paper we introduce a mix norm that is…
We study the spectrum of massive excitations in three-dimensional models belonging to the Ising universality class. By solving the Bethe-Salpeter equation for 3D $\phi^4$ theory in the broken symmetry phase we show that recently found…
We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in…