Bethe-Peierls Approximation for the 2D Random Ising Model
G. Paladin, M. Serva
TL;DR
This paper develops a Bethe-Peierls approximation approach to analyze the partition function of the 2D random Ising model, providing insights into its behavior with disordered couplings.
Contribution
It introduces a novel application of Bethe-Peierls approximations combined with the replica method to the 2D random Ising model's dual lattice.
Findings
Partition function expressed on dual lattice of square plaquettes
Mean field and Bethe-Peierls approximations applied
Insights into disordered 2D Ising model behavior
Abstract
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls approximations, using the replica method.
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