Pion decay constant at finite temperature in the nonlinear σ model

We calculate the pion decay constant near the critical temperature of the $\mathrm{O}(N)$ nonlinear $\ensuremath{\sigma}$ model in the large $N$ limit. Making use of the known low temperature behavior, we construct a Pad\'e approximant to obtain the behavior of ${f}_{\ensuremath{\pi}}(T)$ at all temperatures.