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Finite-time scaling via linear driving: application to the two-dimensional Potts model
Xianzhi Huang1, Shurong Gong, Fan Zhong
1State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Zhongshan University, Guangzhou 510275, People's Republic of China.
Summary
This study uses finite-time scaling to analyze the q-state Potts model, revealing critical properties and exponents. Findings confirm some theoretical predictions while questioning others, suggesting a new method for weak universality characterization.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The q-state Potts model is a fundamental system in statistical mechanics for studying phase transitions.
- Understanding critical phenomena and universality classes is crucial for theoretical physics.
Purpose of the Study:
- To determine the critical properties of the q-state Potts model (q=3, 4) on 2D lattices using finite-time scaling.
- To investigate static and dynamic critical exponents and the critical temperature.
- To explore an alternative method for characterizing weak universality.
Main Methods:
- Application of finite-time scaling to the q-state Potts model with q=3 and 4.
- Introduction of a linearly varying external field to drive the system out of equilibrium.
- Definition of a nonequilibrium order parameter and susceptibility to extract coercive fields.
Main Results:
- Systematic determination of static and dynamic critical exponents and critical temperature.
- Static critical exponents, including the magnetic exponent delta, show reasonable agreement with conjectured values.
- Dynamic critical exponents support dynamic weak universality but show discrepancies with recent short-time dynamic results for q=4.
Conclusions:
- Finite-time scaling provides a robust method for determining critical properties of the Potts model.
- The results offer insights into dynamic weak universality and suggest a novel characterization approach.
- Discrepancies in dynamic exponents highlight areas for further investigation in non-equilibrium statistical mechanics.
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