Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of one-step replica-symmetry-broken phase in satisfiability
  problems   We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two
random combinatorial problems: k-XORSAT and k-SAT. We present a general method
for establishing the stability of these solutions with respect to further steps
of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari
and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general
combinatorial problems.
  It turns out that 1RSB is always unstable at sufficiently small clauses
density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT
is unstable at zero energy for alpha< alpha_m, with alpha_m\approx 4.153. On
the other hand, the SAT-UNSAT phase transition seems to be correctly described
within 1RSB.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys