# Interplay of universality classes in a three-dimensional Yukawa model

## TL;DR

This study numerically explores how different universality classes interact in a three-dimensional Yukawa model with U(1) symmetry, revealing a crossover between fixed points as the Yukawa coupling varies.

## Contribution

It provides the first detailed numerical analysis of the interplay and crossover between magnetic Wilson--Fisher and chiral Gross--Neveu fixed points in the 3D Yukawa model.

## Key findings

- Confirmation of Wilson--Fisher fixed point at zero Yukawa coupling.
- Dominance of chiral Gross--Neveu fixed point at strong Yukawa coupling.
- Observation of crossover behavior with decreasing Yukawa coupling.

## Abstract

We investigate numerically on the lattice the interplay of universality classes of the three-dimensional Yukawa model with U(1) chiral symmetry, using the Binder method of finite size scaling. At zero Yukawa coupling the scaling related to the magnetic Wilson--Fisher fixed point is confirmed. At sufficiently strong Yukawa coupling the dominance of the chiral fixed point associated with the 3D Gross--Neveu model is observed for various values of the coupling parameters, including infinite scalar selfcoupling. In both cases the Binder method works consistently in a broad range of lattice sizes. However, when the Yukawa coupling is decreased the finite size behavior gets complicated and the Binder method gives inconsistent results for different lattice sizes. This signals a cross-over between the universality classes of the two fixed points.