Initial perpendicular isothermal susceptibility formulas for the transverse general-spin Ising and Blume-Capel models

Abstract

Using a Kubo formula and the Suzuki identities, expressions are derived for the initial perpendicular susceptibilities χ_⊥ of the transverse spin-S Ising and spin-S Blume-Capel models on regular and irregular lattices. χ_⊥ is given in terms of the thermal average of a function of the peripheral sumO _i= ε_j J _i,j S _j, where coupling to distant neighbors may be included, as well as arbitrary local parallel magnetic fieldsh _j. For the Ising model on a Bravais lattice, e.g., the susceptibility is given by

$$\chi _ \bot = Nm^2 S^{ - 2} \langle B_s (\beta [O_i + h_i ])/[O_i + h_i ]\rangle $$

whereB _s is the Brillouin function. ForS=1/2, the formula of Fisher and the results of Horiguchi and Morita are regained. A connection is made with the general-spin work of Essam and Garelick.