Low-temperature study of magnetic properties of two-dimensional (2d) classical square Heisenberg lattices

Abstract

We start this article by recalling rigorous results previously obtained for 2d square lattices composed of (2N+1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg couplings), in the thermodynamic limit (N→+∞) [4]: (i) the zero-field partition function Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> (0), (ii) the spin correlation which vanishes in the zero-field limit, except at T=0 K so that the critical temperature is T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> =0 K, in agreement with Mermin-Wagner's theorem, (iii) the spin-spin correlation between any two lattice sites, (iv) the correlation length and (v) the static susceptibility. We exclusively focus on the low-temperature behaviors of the correlation length and the static susceptibility. This leads to the determination of a diagram characterized by three magnetic phases. Moreover we show that all the behaviors are in perfect agreement with the corresponding ones derived by using a renormalization method. Finally we give criterions allowing to directly determine the magnetic phases characterizing 2d magnetic compounds described by our microscopic model. An experimental test is given for illustrating this theoretical study.