Ising Model Spin Correlations on the Triangular Lattice. II. Fourth-Order Correlations

Abstract

A class of fourth-order spin correlations whose sum is closely related to the specific heat is calculated exactly by Pfaffian perturbation theory. In the particular case when the four spins lie on a lattice axis, it is shown that the reduced fourth-order correlation function has the asymptotic form 〈σ0, 0σ1, 1σk, kσk+1, k+1〉−〈σ0, 0σ1, 1〉 〈σk, kσk+1, k+1〉≏A′(e−2βk/k2),where β−1 is the (positive) mean range of order. The decay of correlations with spin separation k is symmetric about the critical point β = 0. The amplitude A′ is 1/π2 at the critical point and is 1/(2π) at all other temperatures. Correlations on ferro- and antiferromagnetic triangular and quadratic lattices are discussed in some detail.