Anomalous distribution of magnetization in an Ising spin glass with correlated disorder

Abstract

The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line in the present model is identical to the distribution function of the spin glass order parameter in the standard Edwards-Anderson model with symmetrically-distributed independent disorder. This result means that if the Edwards-Anderson model exhibits replica symmetry breaking, the magnetization distribution in the correlated model has support on a finite interval, in sharp contrast to the conventional understanding that the magnetization distribution has at most two delta peaks. This unusual behavior challenges the traditional argument against replica symmetry breaking on the Nishimori line in the Edwards-Anderson model. In addition, we show that when temperature chaos is present in the Edwards-Anderson model, the ferromagnetic phase is strictly confined to the Nishimori line in the present model. These findings are valid not only for finite-dimensional systems but also for the infinite-range model, and highlight the need for a deeper understanding of disorder correlations in spin glass systems.

arXiv comment10 pages, 6 figures

References in corpus (68)

• Topological quantum memory
• Statistical physics of inference: Thresholds and algorithms
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Correlated Charge Noise and Relaxation Errors in Superconducting Qubits
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Quantum criticality under decoherence or weak measurement
• Strong Resilience of Topological Codes to Depolarization
• Separation of time and length scales in spin-glasses: temperature as a microscope
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Removing leakage-induced correlated errors in superconducting quantum error correction
• The critical behavior of three-dimensional Ising spin glass models
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Nishimori point in the 2D +/- J random-bond Ising model
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Statistical mechanical models for quantum codes with correlated noise
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• The effect of noise correlations on randomized benchmarking
• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Chaos in temperature in the Sherrington-Kirkpatrick model
• Quantum Error Correction in Spatially Correlated Quantum Noise
• Strong universality and algebraic scaling in two-dimensional Ising spin glasses
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Chaos and Universality in a Four-Dimensional Spin Glass
• Memory and chaos in an Ising spin glass
• Chaos in a Two-Dimensional Ising Spin Glass
• Separability transitions in topological states induced by local decoherence
• Temperature chaos in 3D Ising Spin Glasses is driven by rare events
• Why temperature chaos in spin glasses is hard to observe
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• The critical behavior of 3D Ising glass models: universality and scaling corrections
• Protecting clean critical points by local disorder correlations
• Chaos in spin glasses revealed through thermal boundary conditions
• Coherent error threshold for surface codes from Majorana delocalization
• Symmetry-enforced many-body separability transitions
• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
• Temperature chaos is present in off-equilibrium spin-glass dynamics
• Dynamic Variational Study of Chaos: Spin Glasses in Three Dimensions
• Clifford-deformed Surface Codes
• Limits and performances of algorithms based on simulated annealing in solving sparse hard inference problems
• Surface codes, quantum circuits, and entanglement phases
• Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
• Universality of the glassy transitions in the two-dimensional +- J Ising model
• Universality in p-spin glasses with correlated disorder
• Tapestry of dualities in decohered quantum error correction codes
• Absence of Replica Symmetry Breaking in a Region of the Phase Diagram of the Ising Spin Glass
• Error threshold estimates for surface code with loss of qubits
• Error tolerance of topological codes with independent bit-flip and measurement errors
• The multi-species mean-field spin-glass on the Nishimori line
• Universality in short-range Ising spin glasses
• Chaos in Temperature in Diluted Mean-Field Spin-Glasses
• Disordered Ising model with correlated frustration
• Continuous symmetry breaking along the Nishimori line
• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Ising model formulation for highly accurate topological color codes decoding
• The Random-Bond Ising Model and its dual in Hyperbolic Spaces
• Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs
• Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder
• Gibbs-Bogoliubov inequality on Nishimori line
• Finite-temperature avalanches in 2D disordered Ising models
• Free Energy Evaluation Using Marginalized Annealed Importance Sampling
• Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Statistical Mechanics of Inference in Epidemic Spreading
• A New Monte Carlo Algorithm for Free Energy Calculation
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Exact results on finite size corrections for surface codes tailored to biased noise
• Gauge theory for quantum XYZ spin glasses

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