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Nuclear Physics B - Proceedings Supplements

Exact results for the corner of an Ising ferromagnet

Douglas B. Abraham, F. T. Latrémolière

Published Jan 1, 1996• 1 citation
Publisher
DOI
10.1016/0920-5632(95)00616-8

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Physical Review E•Jan 5, 2015•14 citations
The critical two-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, and fixed double antiferromagnetic. Using bond propagation algorithms with surface fields, we obtain the free energy, internal energy, and specific heat numerically on square lattices with a square shape and various combinations of the four types of boundary conditions. The calculations are carried out on the square lattices with size N×N and 30<N<1000. The numerical data are analyzed with finite-size scaling. The bulk, edge, and corner terms are extracted very accurately. The exact results are conjectured for the corner logarithmic term in the free energy, the edge logarithmic term in the internal energy, and the corner logarithmic term in the specific heat. The corner logarithmic terms in the free energy agree with the conformal field theory very well.