Generalized ice models in two- and three-dimensional lattices: Residual entropies and phase transitions

Abstract

We investigate a family of generalized ice models, employing Wang-Landau Monte Carlo sampling to characterize their residual entropies and thermodynamic behaviors. For the edge-sharing square-ice model, we derive an exact residual-entropy formula. Pauling's approximation yields semiquantitative agreement for corner-sharing systems, typically underestimating residual entropy, but notably overestimating it in the corner-sharing hexagonal-ice model. Thermodynamic analysis reveals that the models with extensive residual entropy exhibit Schottky-type specific heat, without indications of phase transitions, whereas the edge-sharing square-ice and face-sharing cubic-ice models show signatures of continuous and first-order finite-temperature phase transitions, respectively. These results demonstrate how ice-rule constraints give rise to diverse thermodynamic phenomena and offer insights into related frustrated systems.