Renormalization Group Study of the soliton mass on the (lambda Phi^4)_{1+1} lattice model

TL;DR

This paper calculates the soliton mass in the (lambda Phi^4)_{1+1} lattice model using two numerical methods and compares the results with perturbative predictions, emphasizing the importance of the scaling region and continuum limit.

Contribution

It introduces a combined numerical approach to compute the soliton mass and analyzes its continuum limit using Renormalization Group equations, comparing with perturbative results.

Findings

Numerical results for soliton mass are consistent across methods.

The continuum soliton mass slightly exceeds the perturbative one.

Higher order corrections may account for discrepancies.

Abstract

We compute, on the $(\lambda \Phi^4)_{1+1}$ model on the lattice, the soliton mass by means of two very different numerical methods. First, we make use of a ``creation operator'' formalism, measuring the decay of a certain correlation function. On the other hand we measure the shift of the vacuum energy between the symmetric and the antiperiodic systems. The obtained results are fully compatible. We compute the continuum limit of the mass from the perturbative Renormalization Group equations. Special attention is paid to ensure that we are working on the scaling region, where physical quantities remain unchanged along any Renormalization Group Trajectory. We compare the continuum value of the soliton mass with its perturbative value up to one loop calculation. Both quantities show a quite satisfactory agreement. The first is slightly bigger than the perturbative one; this may be due to the contributions of higher order corrections.