Coarsening and percolation in the Ising Model with quenched disorder

TL;DR

This paper investigates the phase ordering dynamics of the 2D Ising Model with quenched disorder, revealing percolating domain structures through large-scale simulations and analysis of winding angles and pair-connectedness.

Contribution

It introduces a detailed numerical study of percolation phenomena in disordered Ising Models, highlighting the role of quenched disorder in domain coarsening.

Findings

Percolating structures emerge during phase ordering.

Disorder influences the geometry of domain patterns.

Winding angle and pair-connectedness are effective analysis tools.

Abstract

Through large-scale numerical simulations, we study the phase ordering kinetics of the $2d$ Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities -- the winding angle and the pair-connectedness -- we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.