Thermodynamics of an extended Fredrickson-Andersen model

Pigorsch, C.; Kimball, J. C.; Frisch, H. L.

doi:10.1103/physreve.59.3196

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…A variation of the SFMs with added "mean-field" facilitation was introduced in [95]: spins can flip if either at least f of their neighbours are up, or if the overall concentration of up-spins in the system is greater than some threshold c th . If the model without the added facilitation is reducible, such as in the case of the 2,1-SFM, then the extended model has a sharp dynamical transition when the concentration of up-spins reaches c th ; for lower concentrations (i.e.…”

Section: Variations On Spin-facilitated Modelsmentioning

confidence: 99%

Glassy dynamics of kinetically constrained models

Ritort

Sollich

2003

Advances in Physics

751

1,055

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We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying "equilibrium glass transition". After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, aging and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.

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Section: Variations On Spin-facilitated Modelsmentioning

confidence: 99%

Glassy dynamics of kinetically constrained models

Ritort

Sollich

2003

Advances in Physics

751

1,055

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“…Moreover, as shown in figure 1, we found that the steady-state values of f A , were appreciably less than those given by equation ( 4), especially as x approaches x c . This is not too surprising, since even for the usual FA model mean-field theory does not provide a very good approximation [14]. In contrast to the steady-state value of f A , the fluctuations δf A = |f A − f A | in f A were found to depend quite strongly on the lattice size, and to increase somewhat in magnitude as x approached x c , while their relative magnitude increases rapidly because of the decrease in f A .…”

Section: Resultsmentioning

confidence: 95%

A modified facilitated kinetic Ising model for supercooled liquids

Halpern

2000

J. Phys.: Condens. Matter

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A modification is considered of the well-known Fredrickson-Andersen facilitated kinetic Ising model for studying the glass transition in supercooled liquids. In this modification, which we call the cluster facilitated kinetic Ising model (CluFKI) model, the flip of a spin between the liquid-like regions represented by A or up states and the solid-like regions represented by B or down states can occur (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n spins in the A state. As a result, the transition from a solid-like to a liquid-like region requires more free volume than the reverse transition, which is physically very reasonable. Computer calculations for the n = 1 CluFKI model, as well as a qualitative analysis, show that as the temperature T of the system decreases, and so the parameter x = E/T increases, the fraction fA of spins in state A when the system is in a metastable steady state decreases until it reaches zero for a critical value xc. Correspondingly, the mean relaxation time ⟨τ⟩ of the system's memory function increases rapidly, and ⟨τ⟩→∞ as x→xc. This behaviour is similar to that for the α-relaxation in supercooled liquids as the glass transition temperature is approached.

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“…The values of x c that we found were between 0.75 and 0.76 for the square lattices and between 1.38 and 1.40 for the cubic lattices, which are much less than those predicted by equation ( 3), as expected. In addition the steady-state values of f A were much less than those predicted by equation ( 2), which is also not surprising, since even for the usual FA model mean-field theory does not provide a good approximation [9].…”

Section: L577mentioning

confidence: 85%

A cluster facilitated kinetic Ising model for supercooled liquids

Halpern¹

1999

J. Phys.: Condens. Matter

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A fundamental modification is considered of the well-known Fredrickson-Andersen (FA) n-spin facilitated kinetic Ising model for studying the glass transition in supercooled liquids, in which the up spins correspond to a liquid-like state A and the down states to a solid-like state B. In our general model, which we call the n-spin cluster facilitated kinetic Ising model, a spin can flip from one state to the other (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n up spins. Thus, in contrast to the FA model, it is easier for an up spin to flip than for one in the down state, which is the physically reasonable motivation for considering this class of models and leads to very different properties. In this communication, we consider the simplest case, namely n = 1, for which both a qualitative analysis and computer simulations show that as the temperature of the system decreases, the fraction f A of spins in state A when the system is in a metastable steady state decreases until it reaches zero at a critical temperature T c , and the mean relaxation time of the system's memory function increases rapidly as T c is approached.

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Thermodynamics of an extended Fredrickson-Andersen model

Cited by 6 publications

References 19 publications

Glassy dynamics of kinetically constrained models

Glassy dynamics of kinetically constrained models

A modified facilitated kinetic Ising model for supercooled liquids

A cluster facilitated kinetic Ising model for supercooled liquids

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