Perpendicular Susceptibility of the Ising Model

A high-temperature expansion of the partition function for a lattice of N spins with Hamiltonian H=−J ∑ (ij)σizσjz−mHz ∑ iσiz−mHx ∑ iσixis derived and thence an expansion for the zero-field perpendicular susceptibility is found. By perturbation theory, χ⊥(T) is also expanded at low temperatures and seen, in general, to increase with T from the value χ⊥(O) = Nm2/q | J |, where q is the coordination number of the lattice. The perpendicular susceptibility is re-expressed in terms of near neighbor pair and higher-order spin correlation functions in zero field. This yields exact closed formulas for the linear chain, the Bethe pseudolattices, and for the plane square and honeycomb lattices. The behavior of χ⊥(T) in the critical region is investigated for these lattices and for the plane superexchange lattice.