Magnetic fluctuations in the classical XY model 0008093英文电子书.pdf

Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system. 1 2∗ 3† 3 3 3 3 S.T. Bramwell , J.-Y. Fortin , P.C.W. Holdsworth , S. Peysson , J.-F. Pinton , B. Portelli , and M. Sellitto 1 Department of Chemistry, University College London, 20 Gordon Street, London, WC1H OAJ, UK 2 Department of Physics, University of Washington, Seattle, USA 3 Laboratoire de Physique, Ecole Normale Sup´erieure de Lyon, 46 All´ee d’Italie, F-69364 Lyon cedex 07, France We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical 0 over the whole of the low temperature phase. It is shown analytically and without recourse to the 0 scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, inde- 0 2 pendent of both system size and critical exponent η . An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high c resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are e calculated and found to be of exponential and double exponential form. The calculated distribution D is fitted to three standard functions: a generalisation of Gumbel’s first asymptote distribution from 2 2 the theory of extremal statistics, a generalised log-normal dis