Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generating function for the connected correlator in the random
  energy model and its effective potential   Starting with two copies of the random energy model coupled with independent
magnetic fields, the generating function for the connected correlator of the
magnetization is exactly derived. Without use of the replica trick, it is shown
that the Hessian of the generating function is symmetric under exchanging the
two copies when the system is finite, but the symmetry is spontaneously broken
in the low-temperature phase. It can be regarded as a rigorous realization of
the replica symmetry breaking. The corresponding effective potential, which has
two independent variables conjugate to the magnetic fields, is also calculated.
It is singular when the two variables coincide. The singularity is consistent
with that observed in the effective potentials of short-ranged disordered
systems in the context of the functional renormalization group.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci