We argue that the analysis of Reimers et al. [Phys. Rev. B 45, 7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromagnet, which suggests a new universality class, is not conclusive. By reanalysis of their data, we demonstrate asymptotic volume dependence in some thermodynamic quantities, which suggests the possibility that the transition may be first order.

In a recent publication Moodera and Meservey concluded from their diffraction data that thin Bi films deposited on a Ni buffer layer have the fcc structure. We point out that the observed diffraction pattern can also be assigned to the common rhombohedral phase with a (102) orientation with respect to the surface.

We explore the topological properties of a modified Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor hopping terms is made unequal and the threefold rotational symmetry C-3 is broken by introducing a dimerization term (vertical bar t(1w(2w))vertical bar < t(1s(2s))) in the Hamiltonian. Using the parameter eta = t(1w)/t(1s) = t(2w)/t(2s), we show that this MHM supports a transition from the quantum anomalous Hall insulator to a higher-order topological insulator (HOTI) phase at eta = +/- 0.5. It also hosts a zero-energy corner mode on a nanodisk that can transition to a trivial insulator without gap closing when the inversion symmetry is broken. The gap-closing critical states are found to be magnetic semimetals with a single Dirac node which, unlike the classic Haldane model, can move along the high-symmetry lines in the Brillouin zone. Our MHM offers a rich tapestry of HOTIs and other topological and nontopological phases.