Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilibrium properties of disordered spin models with two scale
  interactions   Methods for understanding classical disordered spin systems with interactions
conforming to some idealized graphical structure are well developed. The
equilibrium properties of the Sherrington-Kirkpatrick model, which has a
densely connected structure, have become well understood. Many features
generalize to sparse Erdos-Renyi graph structures above the percolation
threshold, and to Bethe lattices when appropriate boundary conditions apply. In
this paper we consider spin states subject to a combination of sparse strong
interactions with weak dense interactions, which we term a composite model. The
equilibrium properties are examined through the replica method, with exact
analysis of the high temperature paramagnetic, spin glass and ferromagnetic
phases by perturbative schemes. We present results of a replica symmetric
variational approximations where perturbative approaches fail at lower
temperature. Results demonstrate novel reentrant behaviors from spin glass to
ferromagnetic phases as temperature is lowered, including transitions from
replica symmetry broken to replica symmetric phases. The nature of high
temperature transitions is found to be sensitive to the connectivity profile in
the sparse sub-graph, with regular connectivity a discontinuous transition from
the paramagnetic to ferromagnetic phases is apparent.

13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas