Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Details Critical Phenomena with Linked Cluster Expansions in a Finite Volume Critical Phenomena with Linked Cluster Expansions in a Finite Volume

1996-04-10

arxiv.org/abs/hep-lat/9604006v1

Physics

High Energy Physics

High Energy Physics - Lattice

36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and tarred tex file hdth9607.tex

Scientific paper

10.1007/BF02181244

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such as Monte Carlo simulations. Our computational tools are illustrated at the example of scalar O(N) models with four and six-point couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.

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