Planar spin chain with competing interactions in an external magnetic field

The 1D classical planar model with nearest neighbor (NN) and next nearest neighbor (NNN) competing interactions is studied at finite temperature in presence of an external magnetic field by the transfer matrix method. In particular we are interested into helix configurations supported by an exchange competition strong enough. The short range order (SRO) is strictly related to the zero temperature long range order (LRO). Our exact calculation makes possible the comparison with the current expectation that a discontinuous helix-fan transition occurs before the continuous fan-collinear transition takes place. This feeling is based on the extrapolation of low field-high field zero temperature expansions. We find strong evidence that this expectation is fulfilled when the turn angle of the helix is lesser than /2, whereas for turn angles greater than /2 the discontinuous transition does not take place and the helix changes continuously to a collinear configuration as the magnetic field is increased. Our conclusion is based on the analysis of the SRO at finite temperature exactly calculated by the transfer matrix method and on the zero temperature exact calculation of the minimum energy of commensurate configurations.