Weak first-order transition and pseudoscaling behavior in the universality class of the $O(N)$ Ising model

Using Monte Carlo and renormalization group methods, we investigate systems with critical behavior described by two order parameters: continuous $($vector$)$ and discrete (scalar). We consider two models of classical three-dimensional Heisenberg magnets with different numbers of spin components $N=1,\dots,4$: the model on a cubic lattice with an additional competing antiferromagnetic exchange interaction in a layer and the model on a body-centered lattice with two competing antiferromagnetic interactions. In both models, we observe a first-order transition for all values of $N$. In the case where competing exchanges are approximately equal, the first order of a transition is close to the second order, and pseudoscaling behavior is observed with critical exponents differing from those of the $O(N)$ model. In the case $N=2$, the critical exponents are consistent with the well-known indices of the class of magnets with a noncollinear spin ordering. We also give a possible explanation of the observed pseudoscaling in the framework of the renormalization group analysis.