  We study the thermodynamic phase transition of a spin Hamiltonian comprising
two 3D magnetic sublattices. Each sublattice contains XY spins coupled by the
usual bilinear exchange, while spins in different sublattices only interact via
biquadratic exchange. This Hamiltonian is an effective model for XY magnets on
certain frustrated lattices such as body centered tetragonal. By performing a
cluster Monte Carlo simulation, we investigate the crossover from the 3D-XY
fixed point (decoupled sublattices) and find a systematic flow toward a
first-order transition without a separatrix or a new fixed point. This strongly
suggests that the correct asymptotic behavior is a first-order transition.
