Non-universal freezing in an alternating-bond Glauber chain

Relaxation in kinetic models on alternating linear chains

A restricted dynamics, previously introduced in a kinetic model for relaxation phenomena in linear polymer chains, is used to study the dynamic critical exponent of one-dimensional Ising models. Both an alternating isotopic chain and an alternating-bond chain are considered. In contrast with what occurs for Glauber dynamics, in these two models the dynamic critical exponent turns out to be the same. The alternating isotopic chain with the restricted dynamics is shown to lead to Nagel scaling for temperatures above some critical value. Further support is given relating the Nagel scaling to the existence of multiple (simultaneous) relaxation processes, the dynamics apparently not playing the most important role in determining such scaling.

Nagel scaling, relaxation, and universality in the kinetic ising model on an alternating isotopic chain

The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.