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

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. 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.

Automated summary

Research has shown that the average energy of the Ising spin glass exhibits no singularity along a specific line in the phase diagram and this result can be extended to cases with correlated disorder. By investigating a type of correlated disorder that suppresses frustration, it is found that the average energy can be expressed as the expectation value of a local gauge variable of the Z(2) gauge Higgs model, indicating no singularity despite the possibility of a phase transition in the subspace. While obtaining an explicit expression for the energy is challenging compared to cases with uncorrelated disorder, an exact closed-form expression for a physical quantity related to the energy is derived in three dimensions using a duality relation.认。