Dynamical origin of the dimensional thermodynamic difference

Investigate whether the qualitative difference between the three-dimensional cubic-lattice and two-dimensional square-lattice Fredrickson–Andersen spin models with kinetic threshold K=2 is associated with corresponding qualitative differences in their dynamical behavior.

Background

The paper studies equilibrium tree-packing configurations of the Fredrickson–Andersen model with kinetic threshold K=2. On the three-dimensional cubic lattice, the authors report a continuous gas–crystal phase transition accompanied by spontaneous symmetry breaking between the two nested cubic sublattices. In contrast, their simulations on the two-dimensional square lattice show no thermodynamic phase transition and a homogeneous disordered gas phase.

The unresolved issue is whether this dimensional contrast in equilibrium thermodynamics also reflects a qualitative contrast in dynamics under the kinetic constraints. Establishing such a relationship would clarify whether the distinct equilibrium behaviors are connected to fundamentally different relaxation or accessibility properties in the two lattice dimensions.