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 e xpansion of the zero-field partition function Z(N)(0) and we recall a numerical treatment which rapidly allows to obtain the other terms; un fortunately, it does not lead to a unique solution. However, in the in finite lattice limit, a single solution is selected and that permits t o derive a closed-form expression for Z(N)(0). We examine its low-temp erature behaviour and we show that the absolute zero plays the role of the critical temperature. Finally, in the high-temperature domain, st arting from the theoretical expression of Z(N)(0), we directly retriev e the result obtained by Rushbrooke and Wood by means of high-temperat ure series expansions. (C) 1998 Elsevier Science B.V. All rights reser ved.