  Some unexpected features of the phase diagram of the monoaxial helimagnet in
presence of an applied magnetic field perpendicular to the chiral axis are
theoretically predicted. A rather general hamiltonian with long range
Heisenberg exchange and Dzyaloshinskii--Moriya interactions is considered. The
continuum limit simplifies the free energy, which contains only a few
parameters which in principle are determined by the many parameters of the
hamiltonian, although in practice they may be tuned to fit the experiments. The
phase diagram contains a Chiral Soliton Lattice phase and a forced
ferromagnetic phase separated by a line of phase transitions, which are of
second order at low T and of first order in the vicinity of the zero-field
ordering temperature, and are separated by a tricritical point. A highly non
linear Chiral Soliton Lattice, in which many harmonics contribute appreciably
to the spatial modulation of the local magnetic moment, develops only below the
tricritical temperature, and in this case the scaling shows a logarithmic
behaviour similar to that at T=0, which is a universal feature of the Chiral
Soliton Lattice. Below the tricritical temperature, the normalized soliton
density curves are found to be independent of T, in agreement with the
experimental results of magnetorresistance curves, while above the tricritical
temperature they show a noticeable temperature dependence. The implications in
the interpretation of experimental results of CrNb3S6 are discussed.
