Ferromagnets from higher $SU(N)$ representations

TL;DR

This paper develops a formalism to analyze the thermodynamics and phase structure of ferromagnets with atoms in arbitrary $SU(N)$ representations, revealing new phases and coexistence phenomena.

Contribution

It introduces a general method for deriving thermodynamics of $SU(N)$ ferromagnets with various irreducible representations, including novel phase coexistence features.

Findings

Symmetric representation yields paramagnetic and ferromagnetic phases with known transition behavior.

Antisymmetric representation exhibits new phases, including coexistence and metastability.

Results are applicable to magnetic systems with reduced symmetry interactions.

Abstract

We present a general formalism for deriving the thermodynamics of ferromagnets consisting of "atoms" carrying an arbitrary irreducible representation of $SU(N)$ and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case.