Momentum Lattice Simulation on a Small Lattice Using Stochastic Quantization

TL;DR

This paper explores stochastic quantization methods for lattice simulations of scalar and gauge theories, analyzing convergence, efficiency, and key physical observables on small momentum lattices.

Contribution

It introduces a second order Langevin algorithm for lattice simulations and compares its performance with first order schemes in scalar and gauge models.

Findings

Second order scheme improves convergence rate

Efficient generation of equilibrium configurations

Analysis of renormalized mass and Wilson loop operators

Abstract

We have studied the scalar $\phi^4$-model in the symmetric phase and the non--compact $U(1)$ gauge theory on a momentum lattice using the Langevin equation for generating configurations. In the $\phi^4$-model we have analyzed the renormalized mass and in the $U(1)$-model we have analyzed the Wilson loop operator. We used a second order algorithm for solving the Langevin equation, and we looked for the convergence rate of the method. We studied the stochastic time needed to generate equilibrium configurations and compared first and second order schemes for both models.