Lattice Independent Approach to Thermal Phase Mixing

TL;DR

This paper introduces a lattice-spacing independent numerical method for simulating finite-temperature scalar field theories, enabling precise analysis of thermal phase transitions in Ginzburg-Landau models.

Contribution

It generalizes previous approaches to achieve results independent of lattice spacing and renormalization scale, specifically applied to thermal phase mixing in scalar field theories.

Findings

Derived lattice-spacing and scale-independent critical parameters.

Proposed a simple procedure for different lattice spacings.

Validated method through application to Ginzburg-Landau models.

Abstract

We show how to achieve lattice-spacing independent results in numerical simulations of finite-temperature stochastic scalar field theories. We generalize the previous approach of hep-lat/9607026 by obtaining results which are independent of the renormalization scale. As an application of our method, we examine thermal phase mixing in the context of Ginzburg-Landau models with short-range interactions. In particular, we obtain the lattice-spacing and renormalization-scale independent critical value of the control parameter which determines the free-energy barrier between the two low-temperature phases. We also propose a simple procedure to extract the critical value of control parameters for different choices of lattice spacing.