Nematic Ordering in the Heisenberg Spin-Glass System in d=3 Dimensions

TL;DR

This paper investigates nematic ordering in a 3D classical Heisenberg spin-glass system with random interactions, revealing a globally aligned nematic phase distinct from local spin-glass order, supported by exact and approximate solutions.

Contribution

It demonstrates the existence of a nematic phase in 3D Heisenberg spin glasses and extends the analysis to higher dimensions, providing phase diagrams and transition temperatures.

Findings

Nematic phase exists in 3D Heisenberg spin glasses.

Global phase diagram includes ferromagnetic, antiferromagnetic, and disordered phases.

Nematic transition temperatures calculated in dimensions 2<d<=4.

Abstract

Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in d=3. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions d>2: We calculate nematic transition temperatures in 24 dimensions in 2<d=<4.