Phase Bifurcations of Strongly Correlated Electron Gas at the Conditions of dHvA Effect

TL;DR

This paper uses catastrophe theory to analyze phase bifurcations in a strongly correlated electron gas under dHvA conditions, revealing how magnetic field variations influence phase transition order and matching experimental observations.

Contribution

It introduces a novel application of catastrophe theory to describe phase bifurcations and transition orders in the electron gas under dHvA conditions, extending standard criteria.

Findings

Discontinuities are described by Riemann-Hugoniot catastrophe.

Standard DPT condition is valid only near the triple degenerate point.

Transition order changes from second to first with magnetic field deviation.

Abstract

In a framework of catastrophe theory we investigate the equilibrium set for the system of strongly correlated electron gas at the conditions of dHvA effect and show that the discontinuities accompanied the diamagnetic phase transition (DPT) is handled by Riemann-Hugoniot catastrophe. We show that applicability of the standard condition for observation of DPT $a\ge$1 where $a$ is the differential magnetic susceptibility is valid only in the nearest vicinity of triple degenerate point corresponding to the center of dHvA period, but for arbitrary value of magnetic field in every period of dHvA oscillations this condition is modified in accordance with the bifurcation set of cusp catastrophe. While at the center of dHvA period the symmetric supercritical pitchfork bifurcation gives rise to the second order phase transition on temperature, the deviation of magnetic field from the value corresponding to the center of dHvA period results in the change of the phase transition order from the second to the first one both on temperature and magnetic field. In the framework of developed theory we obtain good agreement with available experimental data.