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Nature of the phase transition of regularly frustrated vector spin systems inthree dimensions is investigated based on a Ginzburg-Landau-type effectiveHamiltonian. On the basis of the variational analysis of this model, Onoda etal recently suggested the possible occurrence of a chiral phase, where thevector chirality exhibits a long-range order without the long-range order ofthe spin [Phys. Rev. Lett. 99, 027206 (2007)]. In the present paper, weelaborate their analysis by considering the possibility of a first-ordertransition which was not taken into account in their analysis. We find that thefirst-order transition indeed occurs within the variational approximation,which significantly reduces the stability range of the chiral phase, while thechiral phase still persists in a restricted parameter range. Then, we performan extensive Monte Carlo simulation focusing on such a parameter range.Contrary to the variational result, however, we do not find any evidence of thechiral phase. The range of the chiral phase, if any, is estimated to be lessthan 0.1% in the temperature width.

Phase transition of the three-dimensional chiral Ginzburg-Landau model -- search for the chiral phase