Geometrical clusters in two-dimensional random-field Ising models

Abstract

We consider geometrical clusters (i.e. domains of parallel spins) in the square lattice random field Ising model by varying the strength of the Gaussian random field, $Δ$. In agreement with the conclusion of previous investigation (Phys. Rev. E{\bf 63}, 066109 (2001)), the geometrical correlation length, i.e. the average size of the clusters, $ξ$, is finite for $Δ> Δ_c \approx 1.65$ and divergent for $Δ\le Δ_c$. The scaling function of the distribution of the mass of the clusters as well as the geometrical correlation function are found to involve the scaling exponents of critical percolation. On the other hand the divergence of the correlation length, $ξ(Δ) \sim (Δ- Δ_c)^{-ν}$, with $ν\approx 2.$ is related to that of tricritical percolation. It is verified numerically that critical geometrical correlations transform conformally.