Low-temperature properties of a classical zigzag spin chain near the ferromagnet-helimagnet transition point

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.