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De Gruyter eBooks

Computational Evidence for the Transition Point of a Square Ising Lattice with First and Second Neighbour Interactions

W. Bitterlich, Rainer J. Jelitto

Published Dec 31, 1968• 0 citations
Publisher
DOI
10.1515/9783112493168-038

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Computational Evidence for the Transition Point of a Square Ising Lattice with First and Second Neighbour Interactions

W. Bitterlich, Rainer J. Jelitto

Abstract From numerical calculations for a toroidally closed Ising lattice of finite diameter it is seen that it is possible to obtain the transition point of a square Ising lattice with nearest and next‐nearest neighbour interactions to a high degree of accuracy. In the case of a lattice with pure nearest neighbour interactions the curves of the internal energy for all diameters of the torus intersect in one point, which is the transition point of the infinite lattice. When next‐nearest neighbour coupling is present, this is no longer exactly valid, but the dependence of the situation of the different points of intersection on the diameter is so exceedingly weak that a rapid convergence to the Curie point may be assumed with increasing size of the lattice and the transition point can be deduced thereby. The assumptions involved in this method and its consequences are discussed and the result of the investigation is compared with a theory of Vaks et al., which deals with a similar type of interaction.

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A series study of a mixed-spin ferrimagnetic Ising model

J. Oitmaa, Ian Graham Enting

We use both high- and low-temperature series expansions to investigate the phase diagram of a ferrimagnetic mixed-spin S = (1/2,1) Ising model on the square lattice, including an on-site anisotropy term on the S = 1 sites. Evidence is found for a first-order transition for large negative anisotropy, and hence for the existence of a tricritical point. The model, with nearest neighbour interactions only, does not appear to have a ferrimagnetic compensation point.

Journal of Physics Condensed Matter•Nov 17, 2006•32 citations
Abstract From numerical calculations for a toroidally closed Ising lattice of finite diameter it is seen that it is possible to obtain the transition point of a square Ising lattice with nearest and next‐nearest neighbour interactions to a high degree of accuracy. In the case of a lattice with pure nearest neighbour interactions the curves of the internal energy for all diameters of the torus intersect in one point, which is the transition point of the infinite lattice. When next‐nearest neighbour coupling is present, this is no longer exactly valid, but the dependence of the situation of the different points of intersection on the diameter is so exceedingly weak that a rapid convergence to the Curie point may be assumed with increasing size of the lattice and the transition point can be deduced thereby. The assumptions involved in this method and its consequences are discussed and the result of the investigation is compared with a theory of Vaks et al., which deals with a similar type of interaction.