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Journal of Physics A Mathematical and General

Two-dimensional scaling in magnetic systems with non-integer characteristic lengths

Fabio D. A. Aarao Reis

Published Nov 20, 1998• 2 citations
Publisher

Abstract

We studied the ferromagnetic Ising model on two-dimensional finite systems with non-integer characteristic lengths. First we considered very long strips with a finite number I of complete rows and one partially filled row with probability x , which is the two-dimensional version of a layer-by-layer growth. At fixed temperature, when the characteristic length L=I+x increases, the free energy per spin, the specific heat and the magnetic susceptibility oscillate, attaining relative extremes at integer L . The oscillations in the free energy are interpreted as surface corrections related to the oscillations in the mean coordination number. Finite-size scaling relations are not satisfied with continuous L , but still hold for fixed x and variable I , where the differences of mean widths are integers. For fixed x , the fits of the free energy give the conformal anomaly with very good accuracy. We also studied strips with discretized Gaussian distributions of widths, with non-integer means L and rms deviation . In these structures, the thermodynamic quantities vary monotonically with continuous L , but some methods for calculating critical exponents do not work properly when generalized to continuous L . We also obtain with good accuracy in these systems. We discuss the possible implications of our results to real systems behaviour.

DOI
10.1088/0305-4470/31/46/002

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