Fixed-tension partition function of a one-dimensional chain
= Fixed-tension partition function of a one-dimensional chain
{title2=$Z=(2\cosh(\tau a))^n$}
Weighting each configuration by $e^{\tau l}$ gives
$$
Z=(e^{\tau a}+e^{-\tau a})^n
=(2\cosh(\tau a))^n,
\qquad
L=\partial_\tau\log Z=na\tanh(\tau a).
$$