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

arXiv: Disordered Systems and Neural Networks(2019)

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摘要
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.
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