# 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…

## 86 Citations

Kinetically Constrained Models

- Mathematics
- 2009

Kinetically constrained spin models (KCSM) are interacting particle systems which are intensively studied in physics literature as models for systems undergoing glass or jamming transitions. KCSM…

Facilitated spin models: recent and new results

- Physics
- 2009

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from…

Facilitated Oriented Spin Models: Some Non Equilibrium Results

- Physics
- 2008

We perform the rigorous analysis of the relaxation to equilibrium for some facilitated or kinetically constrained spin models (KCSM) when the initial distribution ν is different from the reversible…

Kinetically Constrained Lattice Gases

- Physics
- 2010

Kinetically constrained lattice gases (KCLG) are interacting particle systems which show some of the key features of the liquid/glass transition and, more generally, of glassy dynamics. Their…

Mixing time bounds for oriented kinetically constrained spin models

- Physics
- 2012

We analyze the mixing time of a class of oriented kinetically constrained spin models (KCMs) on a d-dimensional lattice of n sites. A typical example is the North-East model, a 0-1 spin system on the…

Universality for critical kinetically constrained models: infinite number of stable directions

- Mathematics
- 2019

Kinetically constrained models (KCM) are reversible interacting particle systems on Zd with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the…

Exact asymptotics for Duarte and supercritical rooted kinetically constrained models

- Mathematics
- 2018

Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and…

Tracer diffusion at low temperature in kinetically constrained models

- Physics
- 2013

We describe the motion of a tracer in an environment given by a kinetically constrained spin model (KCSM) at equilibrium. We check convergence of its trajectory properly rescaled to a Brownian motion…

Universality Results for Kinetically Constrained Spin Models in Two Dimensions

- MathematicsCommunications in Mathematical Physics
- 2018

Kinetically constrained models (KCM) are reversible interacting particle systems on $${\mathbb{Z}^{d}}$$Zd with continuous timeMarkov dynamics of Glauber type, which represent a natural stochastic…

Kinetically constrained lattice gases: Tagged particle diffusion

- PhysicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2018

Kinetically constrained lattice gases (KCLG) are interacting particle systems on the integer lattice $\mathbb Z^d$ with hard core exclusion and
Kawasaki type dynamics. Their peculiarity is that…

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