Kinetically constrained spin models

@article{Cancrini2006KineticallyCS,
  title={Kinetically constrained spin models},
  author={Nicoletta Cancrini and Fabio Martinelli and Cyril Roberto and Cristina Toninelli},
  journal={Probability Theory and Related Fields},
  year={2006},
  volume={140},
  pages={459-504}
}
We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physics literature as simple models sharing some of the features of the glass transition. KCSM are interacting particle systems on $${\mathbb{Z}}^d$$ with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli(p) measure. The essential feature of a KCSM is that the creation/destruction of a particle at a given site can occur only if the… 
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References

SHOWING 1-10 OF 55 REFERENCES
Jamming Percolation and Glassy Dynamics
We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S. Fisher
Glassy dynamics of kinetically constrained models
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,
Statics and dynamics of the two‐spin–facilitated kinetic Ising model
The two‐spin–facilitated kinetic Ising model, or Fredrickson–Andersen model, in two dimensions is investigated, where down‐spins are energetically favored over up‐spins due to a suitably oriented
The asymmetric one-dimensional constrained Ising model
We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models
Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
TLDR
It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality, and in the ergodic cases the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations.
The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results
AbstractWe study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such
A hierarchically constrained kinetic Ising model
A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric
Facilitated kinetic Ising models and the glass transition
The class of ‘‘facilitated’’ kinetic Ising models introduced in a recent letter is investigated in greater detail. An interpretation of the models in terms of relaxation processes in dense fluids is
Metastability effects in bootstrap percolation ?
Bootstrap percolation models, or equivalently certain types of cellular automata, exhibit interesting finite-volume effects. These are studied here at a rigorous level. We find that for an initial
...
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