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Journal of Physics A Mathematical and General

Finite-size scaling in the (2+1)D Ising model

Chris J. Hamer

Published Apr 21, 1983• 23 citations
Publisher

Abstract

Hamiltonian eigenvalues are calculated for the (2+1)D Ising model on lattices up to 5*5 sites. Finite-size scaling techniques are used to estimate the critical coupling x c =0.329+or-0.001, and index v=0.635+or-0.005. The prospects are discussed for further applications of these methods in three and four dimensions.
DOI
10.1088/0305-4470/16/6/020

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The method of 'symmetrized' stochastic truncation is applied to the (2+1)-dimensional Ising model, to calculate the ground-state energy, mass gap, magnetization and susceptibility on lattices of sizes up to 6*6 sites. The method is shown to be a powerful and accurate Monte Carlo technique, provided the lattice size is not too large, and the model is suitably 'convergent'. Finite-size scaling estimates of the critical indices are nu =0.627(2), alpha =0.12(2), beta =0.324(3), and delta =1.23(1). An estimate of the combination gamma / nu +2 beta / nu =3.000(1) is obtained, in outstanding agreement with the expected hyperscaling relation.