= Finite-ring low-temperature expansion
{title2=$F=-JL-\beta^{-1}\log Q-\beta^{-1}\binom L2(Q-1)e^{-2\beta J}+O_{L,Q}(\beta^{-1}e^{-3\beta J})$}
At fixed finite $L$, the <Helmholtz free energy> of a <periodic Potts chain> receives its first thermal correction from a pair of <domain walls>. The <two-domain-wall degeneracy of a Potts ring> divided by the <ground state> <degeneracy factor> supplies the coefficient. Expanding the exact <canonical partition function> proves the formula. The expansion is not uniform in $L$: taking the <thermodynamic limit> first gives $F/L=-J-\beta^{-1}\log[1+(Q-1)e^{-\beta J}]$, whose leading correction is of order $e^{-\beta J}$.
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