Lattice statistics in a magnetic field. II. Order and correlations of a two-dimensional super-exchange antiferromagnet

Abstract

The long-range order and pair correlation functions of a two-dimensional super-exchange antiferromagnet in an arbitrary magnetic field are derived rigorously from properties of the standard square Ising lattice in zero field. (The model investigated was described in part I: it is a decorated square lattice with magnetic spins on the bonds coupled antiferromagnetically via non-magnetic spins on the vertices.) The behaviour near the transition temperature in a finite field is similar to that of the normal plane lattice, i.e. the long-range orders or spontaneous magnetizations of the sublattices vanish as (T$_t$ - T)$^\frac{1}{8}$ and the pair correlations behave as $\omega_c + W(T - T_t) ln |T - T_t|.$ The configurational entropy is discussed and the anomalous entropy in the critical field at zero temperature is calculated exactly.