Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices
This work addresses a computational challenge in statistical physics for researchers studying spin glass models, but it appears incremental as it builds on existing TAP framework with a new algorithm.
The authors tackled the problem of solving TAP equations for Ising models with random coupling matrices by proposing an iterative algorithm, proving its convergence under the AT criterion in the thermodynamic limit and providing exact analytical expressions for the convergence rate.
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) 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 (AT) criterion is fulfilled. Moreover, we give exact analytical expressions for the rate of the convergence.