Tethered Monte Carlo: computing the effective potential without critical slowing down
Abstract
We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.
Cite
@article{arxiv.0806.0543,
title = {Tethered Monte Carlo: computing the effective potential without critical slowing down},
author = {L. A. Fernandez and V. Martin-Mayor and D. Yllanes},
journal= {arXiv preprint arXiv:0806.0543},
year = {2009}
}
Comments
32 pages, 8 eps figures. Corrected Eq. (36), which is wrong in the published paper