A Comparison of Plane Rotor and Ising Models

Consider Ising spins Sn = ±1interacting under a i3R(2~m)>ln(1 +~,fi) = 0.88137..., hamiltonian H — ~ J~~ with >0 let < denote expectations in this model at inverse temperato be compared with the mean field value 0.5 (which ture 13. Let ç = (c~),a~2))= (cos°a’sin On) be twowas known [21* 1 to be a lower bound on 13~), the component uniformly distributed unit vectors and let gaussian value 2/ir = 0.637 and the value 1.11 ±0.04