Memory-free dynamics for the Thouless-Anderson-Palmer equations of Ising models with arbitrary rotation-invariant ensembles of random coupling matrices.

Çakmak, Burak; Opper, Manfred · Phys Rev E · 2019

basic_science · Level V

Where this comes from

Abstract

We propose an iterative algorithm for solving the Thouless-Anderson-Palmer equations of Ising models with arbitrary rotation-invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical functional method that the proposed algorithm converges when the so-called de Almeida Thouless criterion is fulfilled. Moreover, we give exact analytical expressions for the rate of the convergence.