Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stability of the Replica Symmetric State in Finite Dimensional Spin
  Glasses   According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph