Energy density correlation function of the Ising model in small magnetic fields for T > Tc

Abstract

We examine the energy density correlation function 〈 σ00σ01σMNσMN+1〉 − 〈σ00σ01〉2 of the 2-dimensional Ising model in a small magnetic field. In particular we study the limit T → Tc+, H → 0 and R → ∞ where h = const H|T−Tc|−158 is fixed while r = R|T−Tc| is fixed and large. We find that in order h2 the rescaled density correlation function is d(r, h) − d(r, 0) = h2π−1(2 − 3√3)2K0(r) + O(e−(1+e)r). The functional dependence K0(r) is that predicted by scaling theory.