Third law of thermodynamics and the shape of the phase diagram for systems with a first-order quantum phase transition

TL;DR

This paper explores how the Third Law of Thermodynamics influences the phase diagram of systems with first-order quantum phase transitions, revealing general constraints and specific geometric features.

Contribution

It derives general thermodynamic constraints on phase diagrams with quantum phase transitions, emphasizing the role of the Third Law and analyzing the shape of coexistence curves and tricritical wings.

Findings

Coexistence curve has an infinite slope at T=0.

Tricritical wings are perpendicular to the T=0 plane.

Results are based solely on thermodynamic principles.

Abstract

The Third Law of Thermodynamics constrains the phase diagram of{systems with a first-order quantum phase transition. For zero conjugate field, the coexistence curve has an infinite slope at T=0. If a tricritical point exists at T>0, then the associated tricritical wings are perpendicular to the T=0 plane, but not to the zero-field plane. These results are based on the third law and basic thermodynamics only, and are completely general. As an explicit example we consider the ferromagnetic quantum phase transition in clean metals, where a first-order quantum phase transition is commonly observed.