Mechanisms driving alteration of the Landau state in the vicinity of a second-order phase transition

TL;DR

This paper investigates how the Landau state in a Fermi system changes near a second-order phase transition, revealing that a bifurcation causes a qualitative shift in the state before the transition fully occurs.

Contribution

It demonstrates that the Landau state undergoes a bifurcation-driven transformation, which can be interpreted as a first-order transition, prior to the second-order phase transition.

Findings

Bifurcation in the equation $\epsilon(p)=\mu$ triggers state alteration.

Rearrangement of the Fermi surface occurs before the collective mode collapse.

The transformation can be viewed as a first-order phase transition.

Abstract

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation $\epsilon(p)=\mu$, a condition that ordinarily has the Fermi momentum $p_F$ as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition.