Heisenberg model with long range interaction

Abstract

The functional Integral method as used by Siegert in his study of the Ising Model with long range interaction, is generalized and applied to the Heisenberg model. Above the Bragg-Williams Curie point, the functional integral expression for the partition function is evaluated by a saddle point approximation. This gives us an expansion in powers of the reciprocal range of the interaction which is essentially identical with the Ising Model result, in agreement with Brout who used a ring summation approximation. The expansion is not valid through the Curie point, and in its present form, our method seems to be incapable of giving spin waves. © 1965.