Finite-size critical fluctuations in microscopic models of mode-coupling theory

Franz, Silvio; Sellitto, Mauro

doi:10.1088/1742-5468/2013/02/p02025

Cited by 14 publications

(19 citation statements)

References 27 publications

(54 reference statements)

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“…It is well known that many aspects of dynamical Mode Coupling Theory-like transitions [11], including dynamical heterogeneities and growth of correlations, can be seen studied from the quenched potential construction [12][13][14][15][16]. Using the overlap as an order parameter, as it is done in the annealed and quenched potential cases, allows to discriminate the thermodynamic view of the glass transition, where the overlap among configurations is the relevant order parameter, from a purely kinetic one, where the overlap does not allow to discriminate different metastable states [17,18].…”

Section: Introductionmentioning

confidence: 99%

Universality classes of critical points in constrained glasses

Franz

Parisi

2013

J. Stat. Mech.

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We analyze critical points that can be induced in glassy systems by the presence of constraints.These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in absence of constraints. Through a deep analysis of the soft modes appearing in the replica field theory we can establish the universality class of these points. In the case of the "annealed potential" of a symmetric coupling between two copies of the system, the critical point is in the Ising universality class. More interestingly, is the case of the "quenched potential" where the a single copy is coupled with an equilibrium reference configuration, or the "pinned particle" case where a fraction of particles is frozen in fixed positions. In these cases we find the Random Field Ising Model (RFIM) universality class. The effective random field is a "self-generated" disorder that reflects the random choice of the reference configuration. The RFIM representation of the critical theory predicts non-trivial relations governing the leading singular behavior of relevant correlation functions, that can be tested in numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Universality classes of critical points in constrained glasses

Franz

Parisi

2013

J. Stat. Mech.

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“…58 Finally, the dynamics of the kinetically constrained Fredrickson-Andersen model 59 was analyzed on a Bethe lattice, showing the presence of a dynamical transition whose finite size-scaling is consistent with that of the RFIM. 60 The Fredrickson-Andersen model on a Bethe lattice was also studied in the presence of a random pinning. 61 Strong evidence was then found for the existence of a line c d (T ) of dynamical glass transitions with the characteristic A 2 MCT singularity ending in a critical point with an A 3 MCT singularity related to the dynamical behavior of the RFIM (see above).…”

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confidence: 99%

Random-field Ising-like effective theory of the glass transition. I. Mean-field models

Biroli

Cammarota

Tarjus³

et al. 2018

Phys. Rev. B

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In this paper and in the companion one 1 we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems-the overlap field with an equilibrium reference configuration-close to the putative thermodynamic glass transition. Our starting point is the mean-field theory of glass formation which relies on the existence of a complex free-energy landscape with a multitude of metastable states. In this paper, we focus on archetypal mean-field models possessing this type of free-energy landscape and set up the framework to determine the exact effective theory. We show that the effective theory at the mean-field level is generically of the random-field + random-bond Ising type. We also discuss what are the main issues concerning the extension of our result to finite-dimensional systems. This extension is addressed in detail in the companion paper.

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“…Second, the theoretical analysis of the model on a Bethe lattice will be performed in order to enhance the understanding of the universality of freezing transitions in KCMs. A concrete question on Bethe lattices is whether the singular behaviour of the freezing transitions observed here can be characterized by power-law exponents associated with a mode-coupling equation, as discussed in the Fredrickson-Andersen model [18,26,27,28,29,30,31]. If the answer is yes, since it is different from the Vogel-Fulcher type singularity, we will clarify the origin of the difference between the behaviours of the model on the Bethe lattice and on the square lattice.…”

Section: Discussionmentioning

confidence: 84%

Jamming Transition in Kinetically Constrained Models with Reflection Symmetry

Ohta

Sasa

2014

J Stat Phys

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A class of kinetically constrained models with reflection symmetry is proposed as an extension of the Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezing transition at a non-trivial density. It is conjectured by numerical experiments that the known mechanism of the singular behaviors near the freezing transition in a previously studied model (spiral model) is not responsible for that in the proposed model. KeywordsLattice theory and statistics · Theory and modeling of the glass transition · Percolation PACS 05.50.+q · 64.70.Q-· 64.60.ah IntroductionAthermal particles with repulsive interactions exhibit rigidity with an amorphous structure when the density of the particles is higher than a critical value. Such a phenomenon is referred to as a jamming transition, and elucidation of the nature of jamming transitions is a challenging problem in statistical physics [1,2,3,4,5,6,7,8]. Thus far, the replica theories and the related cavity methods for equilibrium glass models have provided insights into jamming transitions as well as glass transitions [9,10]. As a different approach, kinetically constrained models (KCMs), which were investigated with a physical picture that glassy dynamics is purely kinematic [11,12,13], have been considered for understanding jamming transitions [14]. A particular property of KCMs is the absence of singularities in the equilibrium properties. Nevertheless, dynamical phase transitions in KCMs on Bethe lattices have been known to be strongly connected to a certain dynamical phase transition called a freezing transition in equilibrium glass models [15]. Also, recent studies have attempted to reveal the relationship between KCMs and glass-forming materials [16,17].Let us review theoretical studies on KCMs in brief. Here, we generally call dynamical phase transitions in KCMs freezing transitions, which mean the transition from an equilibrium phase to a frozen phase where an infinite number of particles are at rest as a result of blocking by other particles. The first proof for the existence of a freezing transition was presented for the Fredrickson-Andersen (FA) model and then also the Kob-Andersen model on a Bethe lattice [18,19]. However, for these models in finite dimensions, it has been shown that there are no true phase transitions [19,20], even though the numerical simulations have shown an indication of a transition. Then, it has been proved that a KCM, which is called spiral model, exhibits a freezing transition in two dimensions [21,22], leading to the concept of universality classes (we call that of the spiral model spiral class) for finite-dimensional freezing transitions.

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Finite-size critical fluctuations in microscopic models of mode-coupling theory

Cited by 14 publications

References 27 publications

Universality classes of critical points in constrained glasses

Universality classes of critical points in constrained glasses

Random-field Ising-like effective theory of the glass transition. I. Mean-field models

Jamming Transition in Kinetically Constrained Models with Reflection Symmetry

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