A theory of solving TAP equations for Ising models with general invariant random matrices
A theory of solving TAP equations for Ising models with general invariant random matrices
复制标题
具有一般不变随机矩阵的伊辛模型TAP方程的求解理论
DOI：
10.1088/1751-8113/49/11/114002
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
O. Winther
中科院分区：
文献类型：
--
作者：
M. Opper;Burak Çakmak;O. Winther
我们考虑通过迭代 Ising 模型求解 TAP 平均场方程的问题，该模型具有从一般不变系综中随机抽取的耦合矩阵。我们使用动态函数方法开发迭代算法的分析，该方法在热力学极限下产生单变量轨迹的有效动力学。我们的主要新颖贡献是一般不变系综动力学的隐式记忆项的表达。通过减去这些依赖于先前时间步的磁化强度的项，隐式记忆项被取消，使得迭代仅依赖于高斯分布场。如果满足 de Almeida-Thouless 稳定性准则，则 TAP 磁化强度是稳定的固定点。我们明确地说明了从随机正交系综中提取的耦合矩阵的方法。
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.