Study of the magnetic properties of two-dimensional (2D) classical square heisenberg antiferromagnets II- spin correlations and susceptibility

In this part labelled II we examine the spin correlations and the susceptibility. We use a similar method which has allowed to derive a closed-form expression of the zero-field partition function Z_N(0), for 2D square lattices composed of (2N+1)² classical spins isotropically coupled [1]. We rigorously show that the spin correlation vanishes in the zero-field limit, except at T=0 K. Thus, the critical temperature is T_C=0 K, in agreement with Mermin-Wagner´s theorem. For calculating the spin-spin correlation, we show that it is necessary to distinguish a correlation domain in which the correlation path is confined and a wing domain (Theorem 1). In the thermodynamic limit (N→+∞), we give a general closed-form expression for the spin-spin correlation between any two lattice sites. We prove that all the possible paths have the same analytic expression and correspond to the shortest ones in agreement with the classical principle of least action and its quantum version (Theorem 2). As a result and for the first time, we derive the closed-form expression for the susceptibility, without any approximation. We finally test previous experimental fits and we show that the use of a truncated expansion for the susceptibility was totally justified.