Scalar Field Theory with a Non-Standard Potential

TL;DR

This paper investigates the phase structure of a 4D complex scalar field with a non-standard potential, analyzing its behavior at zero and finite temperatures using mean field and Monte Carlo methods.

Contribution

It introduces a study of a novel scalar field potential and explores its phase transitions and universality class through computational methods.

Findings

Zero-temperature theory aligns with 4D Ising universality class.

Mass of the first excitation remains temperature independent.

Unclear behavior at high temperatures and varying Lambda.

Abstract

We study the phase structure of a 4D complex scalar field theory with a potential V(Phi) = | Lambda^3 / Phi - Lambda Phi |^2 at zero and at finite temperature. The model is analyzed by mean field and Monte Carlo methods. At zero temperature the theory falls in the universality class of the 4D Ising model when varying Lambda. The situation is less clear-cut for variations w.r.t. Lambda at large temperatures and variations w.r.t. temperature at a given value of Lambda. We observe temperature independence of the mass of the first excitation.