Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism
2011
Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total magnitude (system+reservoir) is conserved. The reservoir is actually integrated out, which leaves us with a fluctuation-dissipation formalism that allows us to recover the appropriate Helmholtz effective potential with great accuracy. These methods are demonstrating a remarkable flexibility. In fact, we illustrate two very different applications: hard spheres crystallization and the phase transition of the diluted antiferromagnet in a field (the physical realization of the random field Ising model). The tethered approach holds the promise to transform cartoon drawings of corrugated free-energy landscapes into real computations. Besides, it reduces the algorithmic dynamic slowing-down, probably because the conservation law holds non-locally.
Keywords:
- Computational physics
- Dynamic Monte Carlo method
- Monte Carlo molecular modeling
- Kinetic Monte Carlo
- Quantum mechanics
- Diffusion Monte Carlo
- Quantum Monte Carlo
- Monte Carlo method
- Statistical physics
- Hybrid Monte Carlo
- Monte Carlo method in statistical physics
- Physics
- Monte Carlo integration
- Helmholtz free energy
- Correction
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