  Critical behavior of three-dimensional classical frustrated antiferromagnets
with a collinear spin ordering and with an additional twofold degeneracy of the
ground state is studied. We consider two lattice models, whose continuous limit
describes a single phase transition with a symmetry class differing from the
class of non-frustrated magnets as well as from the classes of magnets with
non-collinear spin ordering. A symmetry breaking is described by a pair of
independent order parameters, which are similar to order parameters of the
Ising and O(N) models correspondingly. Using the renormalization group method,
it is shown that a transition is of first order for non-Ising spins. For Ising
spins, a second order phase transition from the universality class of the O(2)
model may be observed. The lattice models are considered by Monte Carlo
simulations based on the Wang-Landau algorithm. The models are a ferromagnet on
a body-centered cubic lattice with the additional antiferromagnetic exchange
interaction between next-nearest-neighbor spins and an antiferromagnet on a
simple cubic lattice with the additional interaction in layers. We consider the
cases N=1,2,3 and in all of them find a first-order transition. For the N=1
case we exclude possibilities of the second order or pseudo-first order of a
transition. An almost second order transition for large N is also discussed.
