Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Phase Transitions Associated to Topological Lattice Field
  Theories in Dimension $D\ge 2$   We investigate the neighborhood of Topological Lattice Field Theories (TLFTs)
in the parameter space of general lattice field theories in dimension $D\geq
2$, and discuss the phase structures associated to them. We first define a
volume-dependent TLFT, and discuss its decomposition to a direct sum of
irreducible TLFTs, which cannot be decomposed anymore. Using this decomposed
form, we discuss phase structures and renormalization group flows of
volume-dependent TLFTs. We find that TLFTs are on multiple first order phase
transition points as well as on fixed points of the flow. The phase structures
are controlled by the physical states on $(D-1)$-sphere of TLFTs. The flow
agrees with the Nienhuis-Nauenberg criterion. We also discuss the neighborhood
of a TLFT in general directions by a perturbative method, so-called cluster
expansion. We investigate especially the $Z_p$ analogue of the Turaev-Viro
model, and find that the TLFT is in general on a higher order discrete phase
transition point. The phase structures depend on the topology of the base
manifold and are controlled by the physical states on topologically non-trivial
surfaces. We also discuss the correlation lengths of local fluctuations, and
find long-range modes propagating along topological defects. Thus various
discrete phase transitions are associated to TLFTs.

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex