Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coexistence of localized Gibbs measures and delocalized gradient Gibbs
  measures on trees   We study gradient models for spins taking values in the integers (or an
integer lattice), which interact via a general potential depending only on the
differences of the spin values at neighboring sites, located on a regular tree
with d + 1 neighbors. We first provide general conditions in terms of the
relevant p-norms of the associated transfer operator Q which ensure the
existence of a countable family of proper Gibbs measures. Next we prove
existence of delocalized gradient Gibbs measures, under natural conditions on
Q. This implies coexistence of both types of measures for large classes of
models including the SOS-model, and heavy-tailed models arising for instance
for potentials of logarithmic growth.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat