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Finite-Time Dynamical Phase Transition in Nonequilibrium Relaxation
Jan Meibohm1, Massimiliano Esposito1
1Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
Physical Review Letters
|April 1, 2022
Summary
We discovered a finite-time dynamical phase transition in magnetic models, marked by a singularity in magnetization. This transition reveals a sudden dynamic switch and connects to equilibrium phase transitions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Dynamical Systems Theory
Background:
- Understanding thermal relaxation dynamics is crucial for magnetic systems.
- Mean-field models provide a simplified framework for studying complex magnetic phenomena.
- Dynamical phase transitions represent abrupt changes in system behavior over time.
Purpose of the Study:
- To investigate the existence and characteristics of a finite-time dynamical phase transition in a mean-field magnetic model.
- To develop a theoretical framework describing this transition.
- To explore the relationship between dynamical and equilibrium phase transitions.
Main Methods:
- Analysis of a mean-field magnetic model.
- Identification of a cusp singularity in the magnetization's probability distribution.
- Derivation of a dynamical Landau theory.
- Comparison of dynamical and equilibrium critical exponents.
Main Results:
- A finite-time dynamical phase transition was observed, characterized by a cusp singularity at a critical time.
- A dynamical order parameter was identified, signaling a sudden switch in system dynamics.
- The derived dynamical Landau theory accurately describes the transition for scalar, parity-invariant order parameters.
- An exact mapping between dynamical and equilibrium phase transitions was established near criticality, yielding mean-field critical exponents.
Conclusions:
- The study reveals a novel finite-time dynamical phase transition in magnetic systems.
- The developed dynamical Landau theory offers a general framework for such transitions.
- Further research into saddle point interactions may uncover critical spatiotemporal fluctuations and new dynamical critical phenomena.
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