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Abstract
摘要 |
A defining feature of glassiness is the exceedingly slow dynamics that enforces to work in non-equilibrium conditions. Then, what is the relevance (if any) of equilibrium statistical mechanics? It turns out that a time-length dictionary matches non-equilibrium behavior on infinite samples (at finite times) to equilibrium properties of systems of finite-size .
We are thus lead to study the free-energy landscape of finite systems. Technically, we do it through a free-energy profile (also known as Helmholtz free-energy, or large-deviation functional) that describes the landscape topography as a function of one or more order parameters.
The umbrella-sampling computation of free-energy profiles is customary in Chemical Physics. However, umbrella sampling becomes exceedingly cumbersome when several order parameters are needed. On the other hand, almost by definition, complex landscapes cannot be mapped with a single order parameter. A recent refinement, tethered Monte Carlo, handles easily free-energy profiles depending on several parameters [2]. The major problem is, then, a wise selection of order parameters.
The consideration of free-energy profiles makes it feasible to average over disorder at the same value of the order parameters (rather than same temperature, magnetic field, etc.). In this way, huge statistical fluctuations are tamed, and a clearer picture of the overall behavior is obtained.The approach that we advocate here has recently produced significant progress in several, seemingly unrelated problems: temperature chaos in spin-glasses [3], crystallization in colloidal systems [4], the verification of the Cardy-Jacobsen conjecture in three dimensions [5], or the critical behavior of Random-Field-Ising-model like systems [6]. |
