Glassy Critical Points and Random Field Ising Model

Abstract

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory describing these points can be mapped in the ${\varphi }^4$-Random Field Ising Model. We confirm our analysis studying the finite size scaling of the $p$-spin model defined on sparse random graph, where a fraction of variables is frozen such that the phase transition is of a continuous kind.

The paper has been completely revised. A completely new part with simulations of a p-spin glass model on random graph has been included. An appendix with the Mathematica worksheet used in the calculation of the diagrams has also been added

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Cited by in corpus (16)

• Perspective: The Glass Transition
• Overlap fluctuations in glass-forming liquids
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Random-field-like criticality in glass-forming liquids
• Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis
• Phase transition for quenched coupled replicas in a plaquette spin model of glasses
• Dynamical Landau Theory of the Glass Crossover
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Equilibrium Fluctuations in Mean-field Disordered Models
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• Simple physics of the partly pinned fluid systems
• Large deviations of glassy effective potentials
• Percolation approach to glassy dynamics with continuously broken ergodicity
• Heterogeneous nucleation in the random field Ising model
• Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses
• Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems