Hyper Neural Network as the Diffeomorphic Domain for Short Code Soft Decision Beyound Belief Propagation Decoding Problem

Usatyuk, Vasiliy; Egorov, S. I.

doi:10.1109/ewdts50664.2020.9224643

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2024

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

Nishimori

2022

J. Phys. A: Math. Theor.

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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 Z2 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.

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