Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decimation of the Dyson-Ising Ferromagnet   We study the decimation to a sublattice of half the sites, of the
one-dimensional Dyson-Ising ferromagnet with slowly decaying long-range pair
interactions of the form $\frac{1}{{|i-j|}^{\alpha}}$, in the phase transition
region (1< $\alpha \leq$ 2, and low temperature). We prove non-Gibbsianness of
the decimated measure at low enough temperatures by exhibiting a point of
essential discontinuity for the finite-volume conditional probabilities of
decimated Gibbs measures. Thus result complements previous work proving
conservation of Gibbsianness for fastly decaying potentials ($\alpha$ > 2) and
provides an example of a "standard" non-Gibbsian result in one dimension, in
the vein of similar resuts in higher dimensions for short-range models. We also
discuss how these measures could fit within a generalized (almost vs. weak)
Gibbsian framework. Moreover we comment on the possibility of similar results
for some other transformations.

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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: solv-int