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Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling
Yoshihiko Nishikawa1, Manon Michel2, Werner Krauth2
1Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
Summary
The event-chain Monte Carlo algorithm significantly improves simulations of the Heisenberg model. This advanced method reduces the dynamical critical exponent from 2 to approximately 1, enhancing computational efficiency.
Area of Science:
- Statistical physics
- Computational physics
Background:
- The three-dimensional ferromagnetic Heisenberg model is a fundamental system in statistical mechanics.
- Efficient simulation methods are crucial for studying critical phenomena.
Purpose of the Study:
- To evaluate the performance of the event-chain Monte Carlo algorithm for the Heisenberg model.
- To determine if the algorithm can reduce critical slowing down.
Main Methods:
- Application of the event-chain Monte Carlo algorithm.
- Analysis of autocorrelation functions for magnetic susceptibility, energy, and magnetization.
- Calculation of the dynamical critical exponent (z).
Main Results:
- The event-chain Monte Carlo algorithm is rejection-free and satisfies global balance.
- Autocorrelation functions for magnetic susceptibility and energy yield z≈1 at the critical temperature.
- The algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.
Conclusions:
- The event-chain Monte Carlo algorithm offers significant advantages for simulating the Heisenberg model.
- This method effectively mitigates critical slowing down, enabling more efficient studies of phase transitions.
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