Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions for a class of gradient fields   We consider gradient fields on $\mathbb{Z}^d$ for potentials $V$ that can be
expressed as $$e^{-V(x)}=pe^{-\frac{qx^2}{2}}+(1-p)e^{-\frac{x^2}{2}}.$$ This
representation allows us to associate a random conductance type model to the
gradient fields with zero tilt. We investigate this random conductance model
and prove correlation inequalities, duality properties, and uniqueness of the
Gibbs measure in certain regimes. Moreover, we show that there is a close
relation between Gibbs measures of the random conductance model and gradient
Gibbs measures with zero tilt for the potential $V$. Based on these results we
can give a new proof for the non-uniqueness of gradient Gibbs measures without
using reflection positivity. We also show uniqueness of ergodic zero tilt
gradient Gibbs measures for almost all values of $p$ and $q$ and, in dimension
$d\geq 4$, for $q$ close to one or for $p(1-p)$ sufficiently small.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat