Constraints on the merging of the transition lines at the tricritical point in a wing-structure phase diagram

TL;DR

This paper analyzes the phase diagram of a ferromagnetic system near a tricritical point, showing how the wing edges merge with tangent slopes, providing insights into the structure of quantum phase transitions.

Contribution

It demonstrates that the edges of the wings in the phase diagram merge with tangent slopes at the tricritical point, clarifying the geometric structure of the phase boundaries.

Findings

Wing edges merge with tangent slopes at the tricritical point

Phase diagram features a first-order transition line and wings

Insights into quantum phase transition structures

Abstract

We consider the phase diagram of a ferromagnetic system driven to a quantum phase transition with a tuning parameter $p$. Before being suppressed, the transition becomes of the first order at a tricritical point, from which wings emerge under application of the magnetic field $H$ in the $T$-$p$-$H$ phase diagram. We show that the edge of the wings merge with tangent slopes at the tricritical point.