Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite size Berezinski-Kosterlitz-Thouless transition at grain
  boundaries in solid $^4$He and role of $^3$He impurities   We analyze the complex phenomenology of the Non-Classical Rotational Inertia
(NCRI) observed at low temperature in solid $^4$He within the context of a two
dimensional Berezinski-Kosterlitz-Thouless transition in a premelted $^4$He
film at the grain boundaries. We show that both the temperature and $^3$He
doping dependence of the NCRI fraction (NCRIF) can be ascribed to finite size
effects induced by the finite grain size. We give an estimate of the average
size of the grains which we argue to be limited by the isotopic $^3$He
impurities and we provide a simple power-law relation between the NCRIF and the
$^3$He concentration.

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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: math-ph