Percolation Transition in the random antiferromagnetic spin-1 chain

TL;DR

This paper describes a phase transition in a disordered spin-1 chain using percolation theory, supported by numerical simulations and renormalization group calculations, revealing critical properties of the transition.

Contribution

It introduces a percolation-based framework to understand the phase transition in the disordered spin-1 chain, combining numerical and analytical methods.

Findings

Identification of a percolation transition between topological and singlet phases.

Calculation of exact critical exponents for the transition.

Numerical simulation results supporting the theoretical framework.

Abstract

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.