Driven-dissipative Ising model: An exact field-theoretical analysis

Driven-dissipative many-body systems are difficult to analyze analytically due their non-equilibrium dynamics, dissipation and interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local spontaneous emission, which naturally emerges from the open Dicke in large-detuning limit. Utilizing an adaptation of Suzuki-Trotter quantum-to-classical mapping, develop exact field-theoretical analysis diagrammatic representation spin that can be understood simple scattering picture. With representation, able critical behavior, finite-size scaling effective temperature near respective phase transition. Our formalism further allows detailed study ordered where find "heating" region within becomes negative, thereby exhibiting truly behavior. At transition, two distinct behaviors overdamped underdamped dynamics at generic weakly-dissipative points, respectively. We show behavior is robust against short-range perturbations not artifact mean-field nature model. To treat such perturbations, extend our include coupling waves The approach diagrammatics developed work should prove useful applications systems.