Domain walls and Schramm-Loewner evolution in the random-field Ising model

Institut für Physik, Johannes Gutenberg-Universität Mainz - Staudinger Weg 7, 55128 Mainz, Germany, EU

^a stevenso@uni-mainz.de

Received: 27 April 2011
Accepted: 23 June 2011

Abstract

The concept of Schramm-Loewner evolution provides a unified description of domain boundaries of many lattice spin systems in two dimensions, possibly even including systems with quenched disorder. Here, we study domain walls in the random-field Ising model. Although, in two dimensions, this system does not show an ordering transition to a ferromagnetic state, in the presence of a uniform external field spin domains percolate beyond a critical field strength. Using exact ground-state calculations for very large systems, we examine ground-state domain walls near this percolation transition finding strong evidence that they are conformally invariant and satisfy the domain Markov property, implying compatibility with Schramm-Loewner evolution (SLE_κ) with parameter κ=6. These results might pave the way for new field-theoretic treatments of systems with quenched disorder.