复杂系统中的对数临界慢化：从静态到动态
Logarithmic critical slowing down in complex systems: from statics to dynamics
AI总结：
本文研究复杂系统中序参量为复制重叠矩阵的二阶相变，关注三临界点，证明静态复制理论导致对数时间慢化，并给出与模式耦合理论$A_3$奇点一致的对数衰减参数$\mu$的定量表达式。
摘要：
我们考虑序参量为复制重叠矩阵的二阶相变。我们关注出现在多种平均场模型中、且更一般地描述高阶液-液相变或液-玻璃相变的三临界点。我们证明静态复制理论意味着随时间呈对数衰减的慢化。动力学方程恰好是示意模式耦合理论在$A_3$奇点处对过冷粘性液体所预测的方程，其中参数指数为$\lambda=1$。我们得到了对数衰减参数$\mu$的定量表达式，该表达式以重叠的累积量表示，而这些累积量在实验或数值模拟中是可物理观测的。
英文摘要：
We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order liquid-liquid or liquid-glass transitions. We show that the static replicated theory implies slowing down with a logarithmic decay in time. The dynamical equations turn out to be those predicted by schematic Mode Coupling Theory for supercooled viscous liquids at a $A_3$ singularity, where the parameter exponent is $λ=1$. We obtain a quantitative expression for the parameter $μ$ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations.
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