Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization

TL;DR

This paper investigates Langevin lattice dynamics for a scalar field theory with both additive and multiplicative noise, focusing on lattice renormalization and the complexities introduced by multiplicative noise.

Contribution

It introduces a detailed analysis of lattice renormalization in Langevin dynamics with multiplicative noise in scalar field theories.

Findings

Renormalization procedures for Langevin lattice dynamics are developed.

Multiplicative noise introduces specific subtleties in the renormalization process.

The study enhances understanding of stochastic quantization in scalar fields.

Abstract

We consider the Langevin lattice dynamics for a spontaneously broken lambda phi^4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.