Monte Carlo study of the critical properties of noncollinear Heisenberg magnets: $O(3)\times O(2)$ universality class

Abstract

The critical properties of the antiferromagnetic Heisenberg model on the three-dimensional stacked-triangular lattice are studied by means of a large-scale Monte Carlo simulation in order to get insight into the controversial issue of the criticality of the noncollinear magnets with the $O(3)\times O(2)$ symmetry. The maximum size studied is $384^3$, considerably larger than the sizes studied by the previous numerical works on the model. Availability of such large-size data enables us to examine the detailed critical properties including the effect of corrections to the leading scaling. Strong numerical evidence of the continuous nature of the transition is obtained. Our data indicates the existence of significant corrections to the leading scaling. Careful analysis by taking account of the possible corrections yield critical exponents estimates, $\alpha =0.44(3)$, $\beta =0.26(2)$, $\gamma =1.03(5)$, $\nu =0.52(1)$, $\eta =0.02(5)$, and the chirality exponents ${\beta }_{\kappa }=0.40(3)$ and ${\gamma }_{\kappa }=0.77(6)$, supporting the existence of the $O(3)$ chiral (or $O(3)\times O(2)$) universality class governed by a new `chiral' fixed point. We also obtain an indication that the underlying fixed point is of the focus-type, characterized by the complex-valued correction-to-scaling exponent, $\omega =0.1_{-0.05}^{+0.4}+i0.7_{-0.4}^{+0.1}$. The focus-like nature of the chiral fixed point accompanied by the spiral-like renormalization-group (RG) flow is likely to be the origin of the apparently complicated critical behavior. The results are compared and discussed in conjunction with the results of other numerical simulations, several distinct types of RG calculations including the higher-order perturbative massive and massless RG calculations and the nonperturbative functional RG calculation, and the conformal-bootstrap program.

arXiv commentto appear in Phys. Rev. B

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• First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice