Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite cascades of phase transitions in the classical Ising chain   We report the new exact results on one of the best studied models in
statistical physics: the classical antiferromagnetic Ising chain in a magnetic
field. We show that the model possesses an infinite cascade of thermal phase
transitions (also known as "disorder lines" or geometric phase transitions).
The phase transition is signalled by a change of asymptotic behavior of the
nonlocal string-string correlation functions when their monotonous decay
becomes modulated by incommensurate oscillations. The transitions occur for
rarefied ($m$-periodic) strings with arbitrary odd $m$. We propose a duality
transformation which maps the Ising chain onto the $m$-leg Ising tube with
nearest-neighbor couplings along the legs and the plaquette four-spin
interactions of adjacent legs. Then the $m$-string correlation functions of the
Ising chain are mapped onto the two-point spin-spin correlation functions along
the legs of the $m$-leg tube. We trace the origin of these cascades of phase
transitions to the lines of the Lee-Yang zeros of the Ising chain in
$m$-periodic complex magnetic field, allowing us to relate these zeros to the
observable (and potentially measurable) quantities.

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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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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: hep-lat