Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Percolation-Theoretic Approach to Spin Glass Phase Transitions   The magnetically ordered, low temperature phase of Ising ferro- magnets is
manifested within the associated Fortuin-Kasteleyn (FK) random cluster
representation by the occurrence of a single positive density percolating
cluster. In this paper, we review our recent work on the percolation signature
for Ising spin glass ordering -- both in the short-range Edwards-Anderson (EA)
and infinite-range Sherrington-Kirkpatrick (SK) models -- within a two-replica
FK representation and also in the different Chayes-Machta-Redner two-replica
graphical representation. Numerical studies of the $\pm J$ EA model in
dimension three and rigorous results for the SK model are consistent in
supporting the conclusion that the signature of spin-glass order in these
models is the existence of a single percolating cluster of maximal density
normally coexisting with a second percolating cluster of lower density.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas