Quantum to classical crossover in the 2D easy-plane XXZ model

Abstract

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $\Delta$. In the easy--plane ferromagnetic region $(-1<\Delta <0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(\Delta ,\mathbf{r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.

4 pages, 6 figures, Contribution to the Ising Centennial Colloquium, ICM2000, Belo Horizonte, Brazil, August 2000