Fate of the Hybrid Transition of Bootstrap Percolation in Physical Dimension

Rizzo, Tommaso

doi:10.1103/physrevlett.122.108301

Cited by 17 publications

(19 citation statements)

References 42 publications

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“…By exploiting this connection one could address the relaxation dynamics of multiple glasses, a problem that seems at the moment hardly affordable in mean-field disordered p+q-spin models, as the one-step replica symmetry breaking solution seems to be unstable in this type of systems [26,27]. Also, it would be interesting to investigate, e.g., with the Mlayer construction [28], how multiple glass transitions are possibly avoided in physical dimension [29,30]. This might shed some light on the nature of ergodicity breaking in multiple glasses observed experimentally and numerically in short-range attractive colloids and related systems [15,16,17].…”

Section: Discussionmentioning

confidence: 99%

Selective bootstrap percolation

Sellitto¹

2019

J. Stat. Mech.

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A new class of bootstrap percolation models in which particle culling occurs only for certain numbers of nearest neighbours is introduced and studied on a Bethe lattice. Upon increasing the density of initial configuration they undergo multiple hybrid (or mixed-order) phase transitions, showing that such intriguing phase behaviours may also appear in fully homogeneous situations/environments, provided that culling is selective rather than cumulative. The idea immediately extends to facilitation dynamics, suggesting a simple way to construct one-component models of multiple glasses and glass-glass transitions as well as more general coarse-grained models of complex cooperative dynamics.

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Section: Discussionmentioning

confidence: 99%

Selective bootstrap percolation

Sellitto¹

2019

J. Stat. Mech.

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“…In this paper, we shall see how this method is implemented. We stress that the case of the RFIM is just a particular application of the method that is much more general: A recent application shows that the mean-field hybrid transition of bootstrap percolation does not survive in a finite dimension (30) and it could also be used for spin glasses (with zero or nonzero magnetic field) and for the Anderson transition.…”

Section: [2]mentioning

confidence: 99%

Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature

Angelini

Lucibello

Parisi

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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We apply to the random-field Ising model at zero temperature (T=0) the perturbative loop expansion around the Bethe solution. A comparison with the standard ϵ expansion is made, highlighting the key differences that make the expansion around the Bethe solution much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T=0 renormalization group (RG) fixed point. The latter loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding additional terms that are absent in the ϵ expansion. However, these additional terms are subdominant with respect to the standard, supersymmetric ones; therefore, dimensional reduction is still valid at this order of the loop expansion.

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“…The remaining three parameters α, ∆σ and σ can be computed from the properties of the lattice to which we apply the M -layer construction and from the solution of bootstrap percolation on the Bethe lattice with connectivity c = 4. In section (IV) we will use some recent results on the critical properties of bootstrap percolation [36] to show that for (c = 4, m = 2) we have:…”

Section: A the Model And Stochastic-beta-relaxation Equationsmentioning

confidence: 99%

Solvable Models of Supercooled Liquids in Three Dimensions

Rizzo,

Voigtmann

2019

Preprint

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Mode-Coupling Theory (MCT) provides an accurate quantitative description of many supercooled liquids models in the early stages of dynamical slowing down. In realistic systems the description becomes incorrect approaching the MCT singularity that is eventually avoided and replaced by a crossover. The main open problem is to amend MCT and extend it quantitatively to the crossover region and beyond. We consider a family of models in three dimensions obtained by the application of the M -layer construction to the Fredrickson-Andersen Kinetically-Constrained-Model. We argue that deviations from mean-field MCT predictions in these models are described by the Stochastic-Beta-Relaxation (SBR) equations and compute independently the free parameters of the theory. We show that SBR predictions, obtained by numerical solution of the equations, yield an accurate description of the dynamics as obtained from Monte-Carlo simulations, thus providing the first instance of a model that can be described quantitatively at the glass crossover without any fitting parameter.

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Fate of the Hybrid Transition of Bootstrap Percolation in Physical Dimension

Cited by 17 publications

References 42 publications

Selective bootstrap percolation

Selective bootstrap percolation

Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature

Solvable Models of Supercooled Liquids in Three Dimensions

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