Finite Size Scaling of the Higgs-Yukawa Model near the Gaussian Fixed Point

TL;DR

This paper investigates the finite-size scaling behavior of Higgs-Yukawa models near the Gaussian fixed point, providing a method to analyze phase transitions and universality in these models, especially in the strong coupling regime.

Contribution

It introduces a finite-size scaling approach with derived scaling functions for Higgs-Yukawa models near a Gaussian fixed point, facilitating analysis of phase transitions.

Findings

Scaling functions successfully fit lattice data with few parameters

Method applicable to strong Yukawa coupling regions

Supports universality analysis of phase transitions

Abstract

We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility study of our strategy is performed for the pure scalar theory in the weak-coupling regime. Choosing the on-shell renormalisation scheme gives us an advantage to fit the scaling functions against lattice data with only a small number of fit parameters. These formulae can be used to determine the universality of the observed phase transitions, and thus play an essential role in future investigations of Higgs-Yukawa models, in particular in the strong Yukawa coupling region.