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A note on exclusion statistics parameter and Hausdorff dimension

Wellington da Cruz
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Abstract

We obtain for an anyon gas in the high temperature limit a relation between the exclusion statistics parameter $g$ and the Hausdorff dimension $h$, given by $g=h(2-h)$. The anyonic excitations are classified into equivalence classes labeled by Hausdorff dimension, $h$, and in that limit, the parameter $g$ give us the second virial coefficient for any statistics, $ν$. The anyonic excitations into the same class $h$ get the same value of this virial coefficient.

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Wellington da Cruz. 1998-03-05. A note on exclusion statistics parameter and Hausdorff dimension. https://arxiv.org/abs/cond-mat/9803061

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