We perform Monte Carlo simulations on the body-centered-tetragonal helimagnet with Heisenberg spins which has the same breakdown of symmetry as the STA and must belong to the same universality class. We obtain a second order transition with similar critical exponents showing slight differences, maybe connected to the effects of the periodic boundary conditions imposed in MC simulations. This is in contradiction with the renormalization group studies which predict a first order transition. Using Zumbach's 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.[ postscript.gz]