First-order transition in helimagnetic systems with Heisenberg spins

We perform Monte Carlo simulations on the body-centered-tetragonal helimagnet with Heisenberg spins which has the same breakdown of symmetry as the stacked triangular antiferromagnetic lattices and must belong to the same universality class. We obtain a second-order transition with similar critical exponents showing slight differences, which may be connected to the effects of the periodic boundary conditions imposed on MC simulations. This is in contradiction with the renormalization group (RG) studies which predict a first-order transition. Using Zumbachʹs concept of a complex fixed point we reconcile the difference in behavior between simulation and RG studies and show that the transition should be of first order for an infinite system.