  Low-temperature thermodynamics of the classical frustrated ferromagnetic spin
chain near the ferromagnet-helimagnet transition point is studied by means of
mapping to the continuum limit. The calculation of the partition function and
spin correlation function is reduced to quantum problem of a particle in
potential well. It is shown that exactly at the transition point the
correlation length behaves as $T^{-1/3}$ and the magnetic susceptibility
diverges as $T^{-4/3}$ in the low-temperature limit. Corresponding numerical
factors for the correlation length and the susceptibility is calculated. It is
shown that the low-temperature susceptibility in the helical phase near the
transition point has a maximum at some temperature. Such behavior as well as
the location and the magnitude of the maximum as a function of deviation from
the transition point are in agreement with that observed in several materials
described by the quantum $s=1/2$ version of this model.
