Convergent Dynamics for Solving the TAP Equations of Ising Models with Arbitrary Rotation Invariant Coupling Matrices

摘要

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 of large-systems, 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 obtain an exact analytical expression for the rate of the convergence.