Eur. Phys. J. B 56, 93-105 (2007)
https://doi.org/10.1140/epjb/e2007-00095-5

The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions

¹ Laboratoire de Physique des Matériaux, Université Henri Poincaré, Nancy 1, 54506 Vandœuvre-les-Nancy Cedex, France
² Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
³ Institut für Theoretitsche Physik, Johannes Kepler Universität Linz, 4040 Linz, Austria

Corresponding author: ^a akap@ph.icmp.lviv.ua

Received: 16 October 2006
Revised: 28 February 2007
Published online: 12 April 2007

Abstract

We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of ordering (quasi-long-range order) below a certain temperature and a size-dependent mean value of magnetisation in the low-temperature phase that goes to zero (according to the Mermin-Wagner-Hohenberg theorem) in the thermodynamic limit. We focus our attention on the asymptotic behaviour of the spin-spin correlation function and the probability distribution of magnetisation. The analytic approach is based on the spin-wave approximation valid for the low-temperature regime and an expansion in the parameters which characterise the deviation from completely homogeneous configuration of impurities. We further support the analytic considerations by Monte Carlo simulations performed for different concentrations of impurities and compare analytic and MC results. We present as the main quantitative result of the work the exponent of the spin-spin correlation function power law decay. It is non universal depending not only on temperature as in the pure model but also on concentration of magnetic sites. This exponent characterises also the vanishing of magnetisation with increasing lattice size.