  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$_{\kappa}$) with
parameter $\kappa = 6$. These results might pave the way for new
field-theoretic treatments of systems with quenched disorder.
