Note on the Ising Model with Second-Neighbour and Four-Body Interactions Pertaining to Universality

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Abstract
By making use of exact results on the Ising systems investigated by Vaks et al. and by Fisher, thermostatistical properties of the Ising lattice with second-neighbour and four-body interactions are studied. Transition temperatures of such systems can be obtained exactly and the following facts are proved. In the first place, the critical singularities of the systems with these interactions are the same as those of the ordinary Ising model. Secondly, the critical temperature of the ordinary antiferromagnet on the square lattice is a decreasing function of the magnitude of applied magnetic field. By making use of a dual transformation, it is also shown that second-neighbour and four-body interactions are irrelevant to the critical indices for the system with non-vanishing nearest-neighbour interaction.

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