Perturbative computation of thermal characteristics of the Stoner phase transition

TL;DR

This paper develops a perturbative approach to compute thermal properties of the Stoner phase transition in a fermionic system, providing a systematic way to analyze the phase behavior at low temperatures.

Contribution

It introduces a second-order perturbative expansion of the free energy for spin-1/2 fermions and numerically determines the polarization as a function of temperature and interaction strength.

Findings

Systematic second-order free energy expansion.

Numerical determination of polarization at various conditions.

Insights into the phase transition characteristics.

Abstract

We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic) spin 1/2 fermions interacting through a short-range spin independent repulsive binary interaction potential. We show how to obtain a systematic expansion of the system's free energy depending on the densities $n_+$ and $n_-$ of spin-up and spin-down fermions. In this paper we truncate this expansion at the second order and determine, by numerically minimizing the free energy, the equilibrium proportions of $n_+$ and $n_-$ (that is, the system's polarization) as functions of the temperature, the system's overall density $n = n_+ + n_-$ and the strength of the interaction.