Related papers: Metastability of Glauber dynamics with inhomogeneo…
Consider the complete graph on $n$ vertices. To each vertex assign an Ising spin that can take the values $-1$ or $+1$. Each spin $i \in [n]=\{1,2,\dots, n\}$ interacts with a magnetic field $h \in [0,\infty)$, while each pair of spins $i,j…
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…
We consider Glauber dynamics of classical spin systems of Ising type in the limit when the temperature tends to zero in finite volume. We show that information on the structure of the most profound minima and the connecting saddle points of…
In this paper we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the Configuration Model with a prescribed degree…
We investigate the effect of disorder on the Curie-Weiss model with Glauber dynamics. In particular, we study metastability for spin-flip dynamics on the Erd\H{o}s-R\'enyi random graph $ER_n(p)$ with $n$ vertices and with edge retention…
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…
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 study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of…
In this paper we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let $\b$ denote the inverse…
We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model is an anisotropic version, where the interaction energy takes different values on vertical and on…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged…
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…
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…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what…
We study metastability for Glauber spin-flip dynamics on the $N$-dimensional hierarchical lattice with $n$ hierarchical levels. Each vertex carries an Ising spin that can take the values $-1$ or $+1$. Spins interact with an external…
We study the Glauber dynamics for heavy-tailed spin glasses, in which the couplings are in the domain of attraction of an $\alpha$-stable law for $\alpha\in (0,1)$. We show a sharp description of metastability on exponential timescales, in…
We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…