Second interactions in the Ising and Heisenberg models of ferromagnetism

Abstract

Exact series expansions, valid for general spin and general lattice structure, are derived for the Ising and Heisenberg magnets in which first- and second-neighbour interactions are included. The expansions are developed to order six in reciprocal temperature for the zero field free energy and order five for the zero field susceptibility. Comprehensive tables of high-temperature lattice constants are also given which enable the appropriate series for the following lattices to be written down with ease: face-centred cubic, simple cubic, body-centred cubic, simple quadratic and triangular.