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

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.

6 pages, 6 figures. arXiv admin note: text overlap with arXiv:2202.06049

References in corpus (16)

• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• The spin glass transition of the three dimensional Heisenberg spin glass
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries
• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• The Blume-Capel Model on Hierarchical Lattices: exact local properties
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals
• Spin-chirality decoupling in Heisenberg spin glasses and related systems
• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• Comment on ``Spin-glass transition of the three-dimensional Heisenberg spin glass''
• Quenched-Vacancy Induced Spin-Glass Order
• First-Order to Second-Order Phase Transition Changeover and Latent Heats of q-State Potts Models in d=2,3 from a Simple Migdal-Kadanoff Adaptation
• Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
• Renormalization-Group Theory of the Heisenberg Model in d Dimensions

Cited by in corpus (3)

• Nematic Phase of the n-Component Cubic-Spin Spin Glass in d=3: Liquid-Crystal Phase in a Dirty Magnet
• Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory
• Axial, Planar-Diagonal, Body-Diagonal Fields on the Cubic-Spin Spin Glass in d=3: A Plethora of Ordered Phases under Finite Fields