First-order transitions from singly peaked distributions

Michael E. Fisher

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 15, 2873-2879

Abstract: Suppose that, in the thermodynamic limit, a single-component particle system exhibits a standard first-order transition marked by a jump in the density, ρ, at a chemical potential μσ(T). In grand canonical simulations of model fluids that realize such a transition when L→∞ (where L is the linear dimension of the simulation volume) the presence of the transition is typically signaled by the appearance of a double-peaked structure in the distribution function, PN(T,μσ;L), of the particle number, N. A simple, explicit counterexample is presented, however, that proves, contrary to popular beliefs, that the converse proposition is false: i.e., a single-peaked distribution, PN(T,μσ;L), may, when L→∞, give rise to a first-order transition. Alternatively, the existence of a first-order transition does not imply a double-peaked distribution. Systems that may exhibit such single-peaked, first-order behavior are discussed and a possible route to constructing explicit models exhibiting the phenomenon is described. Strategies to use in simulating such systems are briefly considered in the light of related studies.

Keywords: Phase transitions; Simulations; Thermodynamic limit; Particle-number distributions (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:15:p:2873-2879

DOI: 10.1016/j.physa.2010.02.048

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