Numerical Transfer-Matrix Study of Metastability in the d=2 Ising Model
Abstract
We apply a generalized numerical transfer-matrix method to the 2-d Ising ferro- magnet in a nonzero field to obtain complex constrained free energies. Below certain eigenstates of the transfer matrix are identified as representing a metastable phase. The imaginary parts of the metastable constrained free energies are found to agree with a field-theoretic droplet model for a wide range of fields, allowing us to numerically estimate the average free-energy cost of a critical cluster. We find excellent agreement with the equilibrium cluster free energy obtained by a Wulff construction with the exact, aniso- tropic zero-field surface tension, and we present strong evidence for Gold- stone modes on the critical cluster surface. Our results are also fully con- sistent with average metastable lifetimes from previous Monte-Carlo simula- tions. The study indicates that our constrained-transfer-matrix technique pro- vides a nonperturbative numerical method to obtain an analytic continuation of the free energy around the essential singularity at the first-order transition.
Cite
@article{arxiv.cond-mat/9308019,
title = {Numerical Transfer-Matrix Study of Metastability in the d=2 Ising Model},
author = {C. C. A. Guenther and Per Arne Rikvold and M. A. Novotny},
journal= {arXiv preprint arXiv:cond-mat/9308019},
year = {2009}
}
Comments
12 pages, 2 figures available upon request. RevTex version 3.0. FSU-SCRI-93-97