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As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the case of finite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.
Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the s
Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal ($pm h$) random-field Ising model at the strong disorder regime. We consider simp
We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric f
The three-dimensional bimodal random-field Ising model is investigated using the N-fold version of the Wang-Landau algorithm. The essential energy subspaces are determined by the recently developed critical minimum energy subspace technique, and two
In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated e