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

TL;DR

This paper employs a real-space renormalization group approach to analyze the low-temperature dynamics of kinetically constrained Ising chains, revealing unified critical behavior and crossover phenomena near zero-temperature critical points.

Contribution

It introduces a unified RSRG framework to study dynamical properties of KCICs, including crossover behaviors, near their critical points.

Findings

Unified description of dynamical exponents and lengthscale growth

Prediction of crossover from East-like to FA-like behavior

Agreement with previous results for KCICs

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.