Dynamics as a substitute for replicas in systems with quenched random impurities
Dynamics as a substitute for replicas in systems with quenched random impurities
复制标题
动力学作为具有淬灭随机杂质的系统中的复制品的替代品
DOI：
10.1103/physrevb.18.4913
复制
发表时间：
1978
影响因子：
3.7
通讯作者：
C. Dominicis
中科院分区：
文献类型：
--
作者：
C. Dominicis
在随机自由度上的跟踪可以从头开始执行，而不需要复制，只要使用系统的动态描述。在消除随机自由度后，得到了有效的拉格朗日函数。然后，就像爱德华兹和安德森一样，根据关联函数的时间持久部分来定义序参数。以随机温度体系为例，对有序相中的物态方程进行了全阶刻画。结果表明，该方程含有使最简单解不稳定的序参数的奇次幂。这些项表明，Ma和Rudnick发现的关联函数的t−1 2衰变定律仅限于假定的相变点附近的区域。这种形式主义特别适合于处理有序相中的动力学。
Traces over random degrees of freedom may be performed ab initio, without replicas, provided one is using a dynamic description of the system. An effective Lagrangian is obtained after the random degrees of freedom are eliminated. An order parameter is then defined, à la Edwards and Anderson, in terms of the time-persistent part of the correlation function. Taking a system with random temperature as a model example, we characterize to all orders the equation of state in the ordered phase. It is found that this equation contains odd powers of the order parameter that destabilize the simplest solutions. These terms suggest that the t− 1 2 decay law, found by Ma and Rudnick for the correlation function, is restricted to a region close to the presumed transition point. The formalism is particularly suitable for treating dynamics in the ordered phase.