# Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices

## TL;DR

This paper introduces a memory-free iterative algorithm for solving TAP equations in Ising models with rotation invariant random matrices, proving convergence under the AT criterion and providing explicit convergence rates.

## Contribution

The paper presents a novel memory-free algorithm for TAP equations and analytically characterizes its convergence behavior in the thermodynamic limit.

## Key findings

- Algorithm converges when AT criterion is met
- Explicit formulas for convergence rate are derived
- Applicable to arbitrary rotation invariant ensembles

## Abstract

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.