Analyticity of the energy in an Ising spin glass with correlated disorder

Abstract

The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to the case with correlated disorder. For a class of correlations in disorder that suppress frustration, we show that the average energy in a subspace of the phase diagram is expressed as the expectation value of a local gauge variable of the $Z_2$ gauge Higgs model, from which we prove that the average energy has no singularity although the subspace is likely to have a phase transition on it. This is a generalization of the result for uncorrelated disorder. Though it is difficult to obtain an explicit expression of the energy in contrast to the case of uncorrelated disorder, an exact closed-form expression of a physical quantity related to the energy is derived in three dimensions using a duality relation. Identities and inequalities are proved for the specific heat and correlation functions.

References in corpus (14)

• Error Threshold for Color Codes and Random 3-Body Ising Models
• Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
• Protecting clean critical points by local disorder correlations
• Glassy dynamics as a melting process (On melting dynamics and the glass transition, Part II)
• Universality in p-spin glasses with correlated disorder
• Unsupervised feature learning from finite data by message passing: discontinuous versus continuous phase transition
• Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs
• Fundamental thresholds of realistic quantum error correction circuits from classical spin models
• Disordered Ising model with correlated frustration
• Continuous symmetry breaking along the Nishimori line
• Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture

Cited by in corpus (4)

• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Toward mean-field bound for critical temperature on Nishimori line
• Exact mapping of a spin glass with correlated disorder to the pure Ising model