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.

arXiv comment6 pages, 6 figures. arXiv admin note: text overlap with arXiv:2202.06049

References in corpus (37)

• Energy exponents and corrections to scaling in Ising spin glasses
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Stiffness of the Edwards-Anderson Model in all Dimensions
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• Dynamical simulation of spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses
• The spin glass transition of the three dimensional Heisenberg spin glass
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• Scalings of domain wall energies in two dimensional Ising spin glasses
• Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass
• High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries
• Explicit formulas for heat kernels on diamond fractals
• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• Perfect quantum state transfer on diamond fractal graphs
• Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: global thermodynamics from renormalization group theory
• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field
• Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
• Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d=3 tJ model with quenched disorder
• The Blume-Capel Model on Hierarchical Lattices: exact local properties
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Spin-chirality decoupling in Heisenberg spin glasses and related systems
• Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals
• Analysis of Coined Quantum Walks with Renormalization
• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• Real-Space Renormalization for disordered systems at the level of Large Deviations
• Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass
• Devil's Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions
• Comment on ``Spin-glass transition of the three-dimensional Heisenberg spin glass''
• A Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses
• 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

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• 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