Facilitated spin models in one dimension: a real-space renormalization group study

Abstract

We use a real-space renormalization group (RSRG) to study the low temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical lengthscales, and the behaviour of the excitation density near criticality. For the partially asymmetric chain the RG predicts a crossover, on sufficiently large length and time scales, from East-like to FA-like behaviour. Our results agree with the known results for KCICs obtained by other methods.

13 pages. Extended East model RG to arbitrary block sizes. To appear in Phys. Rev. E

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• Thermodynamics of Coarse Grained Models of Super-Cooled Liquids
• Subdiffusion and dynamical heterogeneities in a lattice glass model
• Duality between random trap and barrier models
• Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid