模耦合理论的临界慢化指数
On the critical slowing down exponents of mode coupling theory
摘要：
给出了一种计算模式耦合理论中临界慢化动力学指数的参数指数$λ$的方法。它独立于动态方法，并基于有效静态场论的公式化。提供了$λ$的表达式，表示为作用展开式的三阶系数，或者等价地表示为六点累积量。应用报告的平均场模型的数量：硬和软变量和完全连接和稀释的相互作用。与Potts玻璃模型、ROM模型、硬自旋和软自旋Sherrington-Kirkpatrick模型以及p自旋模型的已有结果进行了比较。
英文摘要：
A method is provided to compute the parameter exponent $λ$ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of $λ$ in terms of third order coefficients of the action expansion or, equivalently, in term of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully-connected and dilute interactions. Comparisons with existing results for Potts glass model, ROM, hard and soft-spin Sherrington-Kirkpatrick and p-spin models are presented.
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