Antiferromagnetic susceptibility of the plane square and honeycomb ising lattices

Abstract

The antiferromagnetic susceptibilities of the plane square and honeycomb Ising lattices are investigated on the basis of the exact series expansions. By removal of the ferromagnetic singularity and careful extrapolation, expressions are obtained which enable the susceptibility to be evaluated with an accuracy of about 0.5% in the critical region and better than 0.1% for temperatures differing from T_c by more than 7%. In the critical region we find χ(T) = (Nm²/kT) {ξ_c + B[1 − (T_c/T)] ln|1 − (T_c/T)|} where for the plane square lattice ξ_c = 0.1570 and B = 0.280 while for the honeycomb ξ_c = 0.1214 and B = 0.252. As a function of temperature χ displays a rather flat maximum above T_c at T_m = 1.537 T_c for the plane square lattice, and T_m = 1.688 T_c for the honeycomb lattice.