Finite size scaling analysis with linked cluster expansions

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 Φ + Φ theory. We indicate further applications to the electroweak transition. 1 LINKED CLUSTER EXPANSIONS IN THE INFINITE VOLUME Convergent expansions such as linked cluster, hopping parameter or high temperature expansions provide an analytic alternative to Monte Carlo simulations. Originally they have been developed in the infinite volume, meanwhile they have been extended to finite volumes as well [1]. In contrast to generic perturbation theory, hopping parameter expansions (HPEs) are convergent expansions about completely disordered lattice systems. The expansion parameter κ is the coefficient of the (pair) interaction term. Since we calculate free energies and connected correlations in the hopping parameter expansion, we generate linked cluster expansions (LCEs). ∗Talk presented by H. Meyer-Ortmanns †e-mail address: [email protected] ‡Heisenberg fellow, e-mail address: [email protected]