Mean Field Solution of the Random Ising Model on the Dual Lattice

TL;DR

This paper introduces a duality transformation for the d-dimensional random Ising model, expressing its partition function in terms of new variables, and solves the dual model using mean field approximation.

Contribution

It presents a novel duality transformation for the random Ising model and provides a mean field solution for the dual model.

Findings

Partition function expressed via dual variables

Mean field solution obtained for the dual model

New insights into the random Ising model's behavior

Abstract

We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The dual model is solved in the mean field approximation.