The Chiral Potts Spin Glass in d=2 and 3 Dimensions

Abstract

The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.

arXiv comment9 pages, 7 figures, 19 phase diagrams. Final published version

References in corpus (62)

• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Energy exponents and corrections to scaling in Ising spin glasses
• Stiffness of the Edwards-Anderson Model in all Dimensions
• Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities
• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Scalings of domain wall energies in two dimensional Ising spin glasses
• Unraveling Quantum Annealers using Classical Hardness
• Multicritical points for the spin glass models on hierarchical lattices
• Temperature Chaos and Bond Chaos in the Edwards-Anderson Ising Spin Glass : Domain-Wall Free-Energy Measurements
• Chaos in spin glasses revealed through thermal boundary conditions
• Random subcubes as a toy model for constraint satisfaction problems
• Disorder chaos in spin glasses
• Large-scale Monte Carlo simulations of the three-dimensional XY spin glass
• Engineering flat electronic bands in quasiperiodic and fractal loop geometries
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks
• The Blume-Emery-Griffiths Spin Glass and Inverted Tricritical Points
• Evidence for a Genuine Ferromagnetic to Paramagnetic Reentrant Phase Transition in a Potts Spin Glass Model
• High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries
• Chaos and residual correlations in pinned disordered systems
• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses
• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• Chaos in Glassy Systems from a TAP Perspective
• Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
• Relation between Random Walks and Quantum Walks
• Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d=3 tJ model with quenched disorder
• Bond chaos in spin glasses revealed through thermal boundary conditions
• Step-wise responses in mesoscopic glassy systems: a mean field approach
• Origin of the hub spectral dimension in scale-free networks
• Thermal entanglement between non-nearest-neighbor spins on fractal lattices
• Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
• The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow
• Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
• Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder
• On temperature chaos in Ising and XY Spin Glasses
• Bond chaos in the Sherrington-Kirkpatrick model
• Classification of critical phenomena in hierarchical small-world networks
• Zeros of the Potts Model Partition Function on Sierpinski Graphs
• A percolation model with continuously varying exponents
• Quenched-Vacancy Induced Spin-Glass Order
• Log-periodic critical amplitudes: a perturbative approach
• Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
• Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model from Renormalization-Group Theory
• Typical and large-deviation properties of minimum-energy paths on disordered hierarchical lattices
• Infinitely Multiple Steps in Magnetization of Ferro- and Antiferromagnetic Ising Models with Frustration on a Diamond Hierarchical Lattice
• Strange Attractor in the Potts Spin Glass on Hierarchical Lattices
• Real-Space Renormalization Group for Spectral Properties of Hierarchical Networks
• Strong Disorder RG principles within a fixed cell-size real space renormalization : application to the Random Transverse Field Ising model on various fractal lattices
• Spin Wave Excitations in AFe${}_{1.5}$Se${}_2$ (A=K, Tl): Analytical Study
• Exact evaluation of the cutting path length in a percolation model on a hierarchical network
• Ferrimagnetism of dilute Ising antiferromagnets
• Random site dilution properties of frustrated magnets on a hierarchical lattice
• Dynamical barriers of pure and random ferromagnetic Ising models on fractal lattices
• Motif based hierarchical random graphs: structural properties and critical points of an Ising model
• Self-Avoiding Walk on Fractal Complex Networks: Exactly Solvable Cases
• Combinatorial models of rigidity and renormalization
• Equation of State from Potts-Percolation Model of a Solid

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