Microcanonical analysis of small systems
Abstract
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from the entropy. Response functions such as the susceptibility are for example related to the curvature of the entropy surface. Interestingly, physical quantities in the microcanonical ensemble show characteristic properties of phase transitions already in finite systems. In this paper we investigate these characteristics for finite Ising systems. The singularities in microcanonical quantities which announce a continuous phase transition in the infinite system are characterised by classical critical exponents. Estimates of the non-classical exponents which emerge only in the thermodynamic limit can nevertheless be obtained by analyzing effective exponents or by applying a microcanonical finite-size scaling theory. This is explicitly demonstrated for two- and three-dimensional Ising systems.
Cite
@article{arxiv.cond-mat/0504018,
title = {Microcanonical analysis of small systems},
author = {Michel Pleimling and Hans Behringer},
journal= {arXiv preprint arXiv:cond-mat/0504018},
year = {2007}
}
Comments
14 pages, 6 figures, invited talk (M.P.) given at the International Symposion on Structure and Dynamics of Heterogeneous Systems SDHS 2004 in Duisburg November 25-26 2004, to appear in a special issue of Phase Transitions