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Physical review. B, Condensed matter

Spinodals and transfer matrices ind=1models

M. A. Novotny, W. Klein, Per Arne Rikvold

Published Jun 1, 1986• 23 citations
Publisher

Abstract

A transfer-matrix method is used to study metastability with particular emphasis on the classical spinodal present in d=1 models when the interaction range goes to infinity. The ``constrained'' free energy and magnetization as a function of the external magnetic field is found for a number of models. The spinodal is found to be at the magnetic field where the metastable phase encounters a density of eigenvalues which approaches infinity as the interaction range approaches infinity.

DOI
10.1103/physrevb.33.7729

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A transfer-matrix method is used to study metastability with particular emphasis on the classical spinodal present in d=1 models when the interaction range goes to infinity. The ``constrained'' free energy and magnetization as a function of the external magnetic field is found for a number of models. The spinodal is found to be at the magnetic field where the metastable phase encounters a density of eigenvalues which approaches infinity as the interaction range approaches infinity.
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Abstract The aim of this chapter is to describe how transfer matrices can be used to solve one-dimensional classical spin models. The idea is to write down the partition function in terms of a matrix, the transfer matrix. The thermodynamic properties of the model are then wholly described by the eigenspectrum of the matrix. In particular the free energy per spin in the thermodynamic limit depends only on the largest eigenvalue and the correlation length only on the two largest eigenvalues through simple formulae.