Finite Size Scaling Analysis with Linked Cluster Expansions

Details Finite Size Scaling Analysis with Linked Cluster Expansions Finite Size Scaling Analysis with Linked Cluster Expansions

1996-08-02

arxiv.org/abs/hep-lat/9608010v1

Nucl.Phys.Proc.Suppl. 53 (1997) 844-846

Physics

High Energy Physics

High Energy Physics - Lattice

3 pages, 1 figure, Talk presented at LATTICE96(Theoretical Developments)

Scientific paper

10.1016/S0920-5632(96)00798-0

Linked cluster expansions are generalized from an infinite to a finite volume on a $d$-dimensional hypercubic lattice. They are performed to 20th order in the expansion parameter to investigate the phase structure of scalar $O(N)$ models for the cases of $N=1$ and $N=4$ in 3 dimensions. In particular we propose a new criterion to distinguish first from second order transitions via the volume dependence of response functions for couplings close to but not at the critical value. The criterion is applicable to Monte Carlo simulations as well. Here it is used to localize the tricritical line in a $\Phi^4 + \Phi^6$ theory. We indicate further applications to the electroweak transition.

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