Tethered Monte Carlo: computing the effective potential without critical slowing down

TL;DR

Tethered Monte Carlo is a versatile method for calculating the effective potential of order parameters, avoiding critical slowing down, and enabling high-precision results in large lattice systems.

Contribution

The paper introduces Tethered Monte Carlo, a new ensemble-based approach that computes the effective potential without critical slowing down, applicable to models like the 2D Ising.

Findings

No critical slowing down observed for magnetic observables.

High precision results achieved for lattices up to size 1024.

Method validated against exact results in the 2D Ising model.

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.