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Noisy mean field annealing (NMFA) is an algorithm that mimics a coherentIsing machine (CIM), which is an optical system for solving Ising problems. TheNMFA has reproduced the solver performance of the CIM for systems of limitedsize even though it simplifies the interaction between spins with a mean-fieldapproximation. However, recent experiments observing various thermodynamicquantities have revealed that the CIM can capture the phase transitions of thetwo-dimensional Ising models that the mean field cannot capture. This situationleads to a fundamental question as to how well the NMFA can capture thefeatures of the thermodynamic quantities around the phase transition. Thispaper answers that the NMFA reproduces the thermodynamic features of the meanfield, but cannot reproduce the CIM results. This suggests that, in terms ofsampling, the level of performance of the CIM is beyond that of the NMFA.

Thermodynamic quantities of two-dimensional Ising models obtained by noisy mean field annealing and coherent Ising machine