6533b7d5fe1ef96bd12645f6

RESEARCH PRODUCT

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

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We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest are calculated straight-forwardly. In particular, it is shown that forL exceeding a characteristic minimum sizeL min the forthorder cumulantg L (T) exhibits a minimum atT min>T c, withT min−T c∝L −d and the value of the cumulant and the minimum (g(T min)) behaving asg(T min)∝L −d. All cumulantsg L (T) forL≫ξ approximately intersect at a common crossing pointT cross∝L −2d, with a universal valueg(T cross)=1−n/2q, wheren is the order parameter dimensionality. By searching for such a behavior in numerical simulation data, the first order character of a phase transition can be asserted. The usefulness of this approach is shown using data for theq=3,d=3 Potts ferromagnet.