Parity-breaking Ising-like model with Spin-Exchange dynamics

We investigate a parity-breaking Ising-like model with Spin-Exchange dynamics using Wang–Landau algorithm. The computed density of states permits the analysis of thermodynamic observables in equilibrium and transport behavior analogous to symmetric simple exclusion process. We observed a density dependent phase transition, where the transition temperature having a minimum at a critical density ${\rho }_c\approx 0.4$. Below ${\rho }_c$ the system shows a diffusive and weakly localized behavior, while above ${\rho }_c$ strongly localized behavior due to the particle mobility. The parity breaking term increases the fluctuations in particle current at ${\rho }_c$, which suggests competing transport mechanisms. The spin exchange dynamics alone can induce a non zero particle current even in equilibrium. As temperature increases, the particle current behavior transits from an oscillatory regime to a steady state where transport is stabilized. Furthermore, the increase of the parity breaking interaction parameter raises the transition temperature ($T_C$), which supports the role of interaction driven effects. The specific heat capacity for different number of particles diverges near $T_C$. The canonical energy distribution shows single-peaked distribution, combined with this continuous energy change and entropy change, and divergence near $T_C$ in specific heat confirms a second order phase transition.