The phase diagram for the $(\lambda \phi ^{4}+\sigma \phi ^{2})_{2}$ model

TL;DR

This paper derives an exact phase boundary equation for a two-parameter quantum field theory model by reducing it to a one-parameter model, providing insights into phase stability and transition regions.

Contribution

It introduces a method to reduce a two-parameter model to a one-parameter model and derives an exact phase boundary equation for the model.

Findings

Exact phase boundary line between broken and unbroken phases.

Estimates on the stability region of the model.

Reduction technique simplifies analysis of the phase diagram.

Abstract

The two parameter model is reduced to a one parameter model by using simple transformations. Because the separation between different phase regions for a one parameter model is just a point, the equivalence between the two models leads to the exact equation of the line that separates the broken and un-broken phases in the $(\lambda ,\sigma)$ plane. Also, we obtain nontrivial estimates on the stability region for this model.