Nature of the phase transition of regularly frustrated vector spin systems in
three dimensions is investigated based on a Ginzburg-Landau-type effective
Hamiltonian. On the basis of the variational analysis of this model, Onoda et
al recently suggested the possible occurrence of a chiral phase, where the
vector chirality exhibits a long-range order without the long-range order of
the spin [Phys. Rev. Lett. 99, 027206 (2007)]. In the present paper, we
elaborate their analysis by considering the possibility of a first-order
transition which was not taken into account in their analysis. We find that the
first-order transition indeed occurs within the variational approximation,
which significantly reduces the stability range of the chiral phase, while the
chiral phase still persists in a restricted parameter range. Then, we perform
an extensive Monte Carlo simulation focusing on such a parameter range.
Contrary to the variational result, however, we do not find any evidence of the
chiral phase. The range of the chiral phase, if any, is estimated to be less
than 0.1% in the temperature width.Comment: 19 pages, 17 figure