Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hierarchical Random Energy Model   We introduce a Random Energy Model on a hierarchical lattice where the
interaction strength between variables is a decreasing function of their mutual
hierarchical distance, making it a non-mean field model. Through small coupling
series expansion and a direct numerical solution of the model, we provide
evidence for a spin glass condensation transition similar to the one occuring
in the usual mean field Random Energy Model. At variance with mean field, the
high temperature branch of the free-energy is non-analytic at the transition
point.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
9
The categories of this paper are: nlin