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.

10 pages, 6 figures

References in corpus (39)

• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Quantum criticality under decoherence or weak measurement
• 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
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Separability transitions in topological states induced by local decoherence
• 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
• 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
• 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
• Universality in p-spin glasses with correlated disorder
• Universality of the glassy transitions in the two-dimensional +- J Ising model
• Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
• Tapestry of dualities in decohered quantum error correction codes
• Disordered Ising model with correlated frustration
• Continuous symmetry breaking along the Nishimori line
• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• The Random-Bond Ising Model and its dual in Hyperbolic Spaces
• Ising model formulation for highly accurate topological color codes decoding
• Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs
• Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder
• Free Energy Evaluation Using Marginalized Annealed Importance Sampling
• Finite-temperature avalanches in 2D disordered Ising models
• Gibbs-Bogoliubov inequality on Nishimori line
• 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
• 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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