Generalized classical theory of magnetism

Abstract

We consider an Ising model with Kac potential γ^dK(γ¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limitγ→0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀≠0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2π/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.