Symmetry, complexity and multicritical point of the two-dimensional spin glass

Abstract

We analyze models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge Boltzmann factors. It is shown that the applications of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions, suggesting that the system has special simplicities under such conditions. Using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram.

arXiv comment32 pages, 6 figures; a few typos corrected. To be published in J. Phys. A

References in corpus (12)

• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• The two-dimensional random-bond Ising model, free fermions and the network model
• Nishimori point in the 2D +/- J random-bond Ising model
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Universality, frustration and conformal invariance in two-dimensional random Ising magnets
• High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
• Complexity spectrum of some discrete dynamical systems
• Let's Baxterise
• A classification of four-state spin edge Potts models
• Phase diagram and critical exponents of a Potts gauge glass
• Rational dynamical zeta functions for birational transformations
• Derivatives and inequalities for order parameters in the Ising spin glass

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• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Multicritical point of Ising spin glasses on triangular and honeycomb lattices
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• Self-dual random-plaquette gauge model and the quantum toric code
• Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
• Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
• 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
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• Error threshold estimates for surface code with loss of qubits
• Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
• Renormalization Group on hierarchical lattices in finite dimensional disordered Ising and Blume-Emery-Griffiths Models
• Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses
• Duality analysis on random planar lattice
• Universality in phase boundary slopes for spin glasses on self dual lattices
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Self-Duality and Phase Structure of the 4D Random-Plaquette Z_2 Gauge Model
• Multicritical point of spin glasses
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• The Implications of Ignorance for Quantum Error Correction Thresholds
• Multicritical Points of Potts Spin Glasses on the Triangular Lattice
• An extension of estimation of critical points in ground state for random spin systems
• Error counting in a quantum error-correcting code and the ground-state energy of a spin glass
• Efficient ${\mathbb{Z}}_2$ synchronization on ${\mathbb{Z}}^d$ under symmetry-preserving side information