Nonequilibrium Fixed Points of Coupled Ising Models.

Area of Science:

• Statistical Physics
• Quantum Optics
• Condensed Matter Theory

Background:

• Driven-dissipative systems typically exhibit classical equilibrium behavior despite their nonequilibrium origin.
• Understanding genuine nonequilibrium phenomena is crucial for advancing beyond classical physics limitations.

Purpose of the Study:

• To investigate multicritical points in driven-dissipative systems for novel nonequilibrium phenomena.
• To analyze a specific model of interacting bosons exhibiting coupled phase transitions.

Main Methods:

• Utilized a dynamical renormalization-group approach to study critical behavior.
• Analyzed a driven-dissipative model of interacting bosons with ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry.

Main Results:

• Identified emergent nonequilibrium fixed points (NEFPs) governing long-distance critical behavior.
• Observed reduction of continuous scale invariance to discrete scale invariance, leading to complex critical exponents and spiraling phase boundaries.
• Demonstrated violation of the fluctuation-dissipation relation, indicating an effective 'hotter' temperature at longer wavelengths.

Conclusions:

• Multicritical points in driven-dissipative systems are a source of rich, genuinely nonequilibrium behavior.
• The observed phenomena, including discrete scale invariance and violated fluctuation-dissipation relations, offer direct evidence of nonequilibrium physics.
• Proposed cavity arrays with cross-Kerr nonlinearities as a potential experimental platform for observing these effects.