Splitting of nonequilibrium phase transitions in driven Ising models

Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal an innovative phenomenon in which the interplay between different temperatures and driving forces splits the order-disorder transition into two distinct transition points depending on which ordered state initially dominates. Crucially, these two emerging phases have distinct scaling behaviors and thermodynamic properties. To study this, we propose a minimal variant of the Ising model where spins are coupled to two thermal baths and subjected to two opposite driving forces associated with them. Our findings, robust for both all-to-all interactions (where exact solutions are possible) and nearest-neighbor couplings on a square lattice, uncover unique nonequilibrium behaviors and scaling laws for crucial thermodynamic quantities, such as efficiency, dissipation, power and its fluctuations, that are different between the two ordered phases. We also highlight that one of these emerging phases enables heat-engine operations that are less dissipative and show reduced fluctuations. In this setup, the system can also operate near maximum power and maximum efficiency over a wide parameter range. Our results offer unique insights into the relevance of phase transitions under nonequilibrium conditions.