Some Remarks on Perturbation Theory and Critical Phenomena

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Abstract
Thermodynamic perturbation theory is applied to systems that undergo a phase transition. It is shown that certain conditions are necessary in order that the application of the perturbation does not change the qualitative features of the phase transition, e.g., the critical indices. The method is then applied to the two-dimensional-square Ising lattice with nearest-and next-nearest-neighbor interactions. The shift in the critical temperature is determined to two orders in the peturbation parameter, viz., the ratio of the strength of the next-nearest-neighbor force to the strength of the nearest-neighbor force. A similar calculation is also made for a two-dimensional-lattice potential of Kac and Helfand.

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