 01434 Ostap Hryniv and Dima Ioffe
 Selfavoiding polygons:
Sharp asymptotics of canonical partition functions under the fixed
area constraint
(726K, ps)
Nov 26, 01

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Abstract. We study the selfavoiding polygons (SAP) connecting the
vertical and the horizontal semiaxes of the
positive quadrant of $\mathbb{Z}^2$. For a fixed $\beta>0$, assign to
each such polygon $\omega$ the weight $\exp\{\beta\omega\}$,
$\omega$
denoting the length of $\omega$, and consider
the sum $Z_{Q,+}$ of these weights for all SAP enclosing area
$Q>0$. We study the statistical properties of such SAP and, in
particular, derive the exact asymptotics for the partition function
$Z_{Q,+}$ as $Q\to\infty$.
The results are valid for any $\beta >\beta_c$, $\beta_c$ being the
critical value for the 2D selfavoiding walks.
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