The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition are described in the $\beta$ regime by dynamical stochastic equations. The quantitative parameters of the dynamical stochastic equations have been computed analytically on the 3-spin Bethe lattice Spin-Glass by means of the (static) cavity method and the equations have been solved numerically. The resulting parameter-free dynamical predictions are shown here to be in excellent agreement with numerical simulation data for the correlation and its fluctuations.

中文翻译：

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平均场理论之外的随机方程和动力学

在具有复制对称破坏的一步的自旋玻璃模型中发生的动态转变是一种平均场伪影，它在有限系统和/或有限维度中消失。平滑过渡的临界波动通过动态随机方程在 $\beta$ 机制中描述。动力学随机方程的定量参数已经在3自旋Bethe晶格自旋玻璃上通过（静态）腔法解析计算，方程已经数值求解。此处显示所得的无参数动态预测与相关性及其波动的数值模拟数据非常一致。