Fully polarized Fermi systems at finite temperature

TL;DR

This paper models a fully spin-polarized Fermi gas in two and three dimensions, analyzing its thermodynamics, phase transitions, and how quantum effects influence classical phase behavior.

Contribution

It introduces a simplified model for polarized Fermi systems at finite temperature, highlighting the impact of quantum statistics on phase diagrams and transitions.

Findings

Identification of first-order phase transitions in polarized Fermi gases.

Distinct phase diagram features for 2D and 3D systems.

Dependence of phase behavior on interparticle attraction and quantum effects.

Abstract

We propose a simple model of an interacting, fully spin--polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first--order phase transitions between the low and high density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for $d=2$ and $3$, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embeded in the fermionic nature of the system under study.