Nonequilibrium Phase Transition to Temporal Oscillations in Mean-Field Spin Models

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Theoretical Physics

Background:

• Understanding nonequilibrium phase transitions is crucial for complex systems.
• Spin models exhibit rich dynamical behaviors, including oscillations.
• Existing theories often struggle to capture nonequilibrium dynamics.

Purpose of the Study:

• To develop a mean-field theory for nonequilibrium phase transitions to spontaneously oscillating states in spin models.
• To identify the order parameter and characteristics of the oscillating phase.
• To provide an explicit illustration using a kinetic mean-field spin model.

Main Methods:

• Formulating a nonequilibrium generalization of Landau free energy using joint distributions.
• Defining a Hamiltonian as the order parameter for oscillations.
• Analyzing stochastic spin dynamics to determine theoretical parameters.
• Investigating overlap distributions in the oscillating phase.

Main Results:

• A novel mean-field theory for nonequilibrium phase transitions to oscillating states is proposed.
• A Hamiltonian is identified as the order parameter, signaling the onset of oscillations.
• The oscillating phase exhibits a nontrivial overlap distribution, resembling replica symmetry breaking without disorder.

Conclusions:

• The proposed mean-field theory successfully describes the transition to spontaneously oscillating states in spin models.
• The theory highlights the emergence of complex dynamics and order even in the absence of quenched disorder.
• This work provides a framework for studying nonequilibrium phenomena in magnetic systems.