Exactly solvable effective stochastic KCMs

Determine whether there exist one-dimensional stochastic kinetically constrained models for which the effective models generated by the low-temperature stochastic-generator expansion are exactly solvable, as occurs for certain quantum kinetically constrained models.

Background

The paper develops a systematic expansion of the stochastic generator in the low equilibrium excitation concentration for kinetically constrained models, focusing on the one-dimensional East and Fredrickson–Andersen models. Successive truncations produce effective descriptions governing increasingly long relaxation times and reveal nested sets of metastable configurations.

The authors note that these effective models may themselves be of interest as kinetically constrained models. Although the construction is more general than the two examples studied, it remains unresolved whether any one-dimensional stochastic KCMs yield effective models that are exactly solvable, analogous to certain quantum KCMs.