Critical behaviour of magnetic systems with helical state

Abstract
We consider a metamagnet in which the nearest neighbour J1 and next nearest neighbour interlayers interaction J2, compete in such a way that the system reaches a helical‐like ordering. A renormalization group analysis of this model (to all order in ε=−d−4) shows that the critical exponents are Heisenberg‐like, with n=2, 4 for the para↔sinusoidal and para↔planar helical transitions respectively. These results differ from the ones obtained when the helical ordering is due to a Dzyaloshinskii‐Moriya interaction. Boundaries of the phase diagram around the bicritical points are studied by scaling and renormalization group analysis.