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Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

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Abstract

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.

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Authors and Affiliations

  1. Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Zaragoza, Spain

    V. Martin-Mayor, B. Seoane & D. Yllanes

  2. Departamento de Física Teórica I, Universidad Complutense, 28040, Madrid, Spain

    V. Martin-Mayor, B. Seoane & D. Yllanes

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  1. V. Martin-Mayor
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  2. B. Seoane
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  3. D. Yllanes
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Martin-Mayor, V., Seoane, B. & Yllanes, D. Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism. J Stat Phys 144, 554–596 (2011). https://doi.org/10.1007/s10955-011-0261-4

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