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Tethering methods allow us to perform Monte Carlo simulations in ensembleswith conserved quantities. Specifically, one couples a reservoir to thephysical magnitude of interest, and studies the statistical ensemble where thetotal magnitude (system+reservoir) is conserved. The reservoir is actuallyintegrated out, which leaves us with a fluctuation-dissipation formalism thatallows us to recover the appropriate Helmholtz effective potential with greataccuracy. These methods are demonstrating a remarkable flexibility. In fact, weillustrate two very different applications: hard spheres crystallization andthe phase transition of the diluted antiferromagnet in a field (the physicalrealization of the random field Ising model). The tethered approach holds thepromise to transform cartoon drawings of corrugated free-energy landscapes intoreal computations. Besides, it reduces the algorithmic dynamic slowing-down,probably because the conservation law holds non-locally.

Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism