  We introduce and study in two dimensions a new class of dry, aligning, active
matter that exhibits a direct transition to orientational order, without the
phase-separation phenomenology usually observed in this context. Characterized
by self-propelled particles with velocity reversals and ferromagnetic alignment
of polarities, systems in this class display quasi-long-range polar order with
continuously-varying scaling exponents and yet a numerical study of the
transition leads to conclude that it does not belong to the
Berezinskii-Kosterlitz-Thouless universality class, but is best described as a
standard critical point with algebraic divergence of correlations. We
rationalize these findings by showing that the interplay between order and
density changes the role of defects.
