Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical clusters in two-dimensional random-field Ising models   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, $\Delta$. 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, $\xi$, is finite for
$\Delta > \Delta_c \approx 1.65$ and divergent for $\Delta \le \Delta_c$. 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, $\xi(\Delta) \sim (\Delta - \Delta_c)^{-\nu}$, with $\nu \approx 2.$ is
related to that of tricritical percolation. It is verified numerically that
critical geometrical correlations transform conformally.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol