On the Metastability in Three Modifications of the Ising Model

K. Bashiri

2019, v.25, Issue 3

ABSTRACT

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature.
The first model (see Chapter \ref{S2}) is an anisotropic version, where the interaction energy takes different values on vertical and on horizontal bonds.
The second model (Chapter \ref{S4}) adds next-nearest-neighbor attraction to the standard Ising model.
And the third model (Chapter \ref{pm}) associates different alternating signs for the magnetic fields on even and odd rows.
All these models have already been studied, and results concerning metastability have been established using the so-called \textit{path-wise approach} (see \cite{KO92},\cite{KO94},\cite{NO96}).
In this text, we extend these earlier results, and apply the \emph{potential-theoretic approach} to metastability to obtain more precise asymptotic information on the transition time from the metastable phase to the stable phase.

Keywords: metastability, Glauber dynamics, potential-theoretic approach

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