Thermodynamics of the 2D-Heisenberg classical square lattice: Zero-field partition function

We consider a 2D lattice composed of classical spins and characterized by a square unit cell; moreover, each classical moment interacts with its nearest neighbours by means of an isotropic alternating exchange coupling showing a regular distribution over the whole lattice. For a finite lattice, we exactly establish the beginning of the polynomial expansion of the zero-field partition function Z(N)(0) and we recall a numerical treatment which rapidly allows to obtain the other terms; unfortunately, it does not lead to a unique solution. However, in the infinite lattice limit, a single solution is selected and that permits to derive a closed-form expression for Z(N)(0). We examine its low-temperature behaviour and we show that the absolute zero plays the role of the critical temperature. Finally, in the high-temperature domain, starting from the theoretical expression of Z(N)(0), we directly retrieve the result obtained by Rushbrooke and Wood by means of high-temperature series expansions. (C) 1998 Elsevier Science B.V. All rights reserved.