Thermodynamic phase transitions in lattice spin systems with severe kinetic constraints: Numerical simulation results

The Fredrickson-Andersen model with hyperparameter $K=1$ is a severely constrained kinetic lattice spin system, such that any site is temporarily blocked from changing its packing state (empty or occupied) if there is one or more occupied nearest neighbors. Starting from a completely random initial configuration with a fraction $\rho$ of sites being occupied, some of the sites may be permanently frozen to their initial state under this severe kinetic constraint. The remaining sites can switch states at least occasionally, and they form the unfrozen subsystem associated with the given initial configuration. In the present work we investigate thermodynamic phase transitions in such unfrozen subsystems of the two-dimensional square lattice and the three-dimensional cubic lattice by extensive numerical simulations. We demonstrate that the giant connected component of the unfrozen subsystem collapses at certain critical value $\rho_{c}$ of initial packing density, with $\rho_c = 0.2475$ for the square lattice and $\rho_c = 0.2809$ for the cubic lattice. This phase transition belongs to the same universality class of the conventional site percolation. We also observe that the ground states (densest packing configurations) experience a continuous crystal-to-glass phase transition at the critical value $\rho^* = 0.1423$ of initial packing density for the cubic lattice. For the two-dimensional square lattice we argue that long-range crystalline order is destroyed in the ground states as long as the initial packing density $\rho$ is positive.