Comment on "Critical properties of highly frustrated pyrochlore antiferromagnets"

We argue that the analysis of Reimers {\it et al.} [ Phys. Rev. B {\bf 45}, 7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromagnet, which suggests a new universality class, is not conclusive. By re-analysis of their data, we demonstrate asymptotic volume dependence in some thermodynamic quantities, which suggests the possibility that the transition may be first order.Comment: 5 pages (RevTex 3.0), 3 figures available upon request, CRPS-93-0

Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via long range dipole-dipole forces and nearest neighbor exchange. Antiferromagnetic exchange alone is known not to induce ordering in this system. We analyze low temperature order resulting from the combined interactions, both by using a mean-field approach and by examining the energy cost of fluctuations about an ordered state. We discuss behavior as a function of the ratio of the dipolar and exchange interaction strengths and find two types of ordered phase. We relate our results to the recent experimental work and reproduce and extend the theoretical calculations on the pyrochlore compound, Gd$_2$Ti$_2$O$_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59}, 14489 (1999).Comment: 5 pages, 5 figures, AMSLaTe

Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study

Histogram Monte-Carlo simulation results are presented for the magnetic-field -- temperature phase diagram of the XY model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions. Finite-size scaling results at the various transition boundaries are consistent with expectations based on symmetry arguments. Although a molecular-field treatment of the Hamiltonian fails to reproduce the correct structure for the phase diagram, it is demonstrated that a phenomenological Landau-type free-energy model contains all the esstential features. These results serve to complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-

Histogram Monte Carlo study of multicritical behavior in the hexagonal easy-axis Heisenberg antiferromagnet

The results of a detailed histogram Monte-Carlo study of critical-fluctuation effects on the magnetic-field temperature phase diagram associated with the hexagonal Heisenberg antiferromagnet with weak axial anisotropy are reported. The multiphase point where three lines of continuous transitions merge at the spin-flop boundary exhibits a structure consistent with scaling theory but without the usual umbilicus as found in the case of a bicritical point.Comment: 7 pages (RevTex 3.0), 1 figure available upon request, CRPS-93-1

Magnetic-Field Induced First-Order Transition in the Frustrated XY Model on a Stacked Triangular Lattice

The results of extensive Monte Carlo simulations of magnetic-field induced transitions in the xy model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions are discussed. A low-field transition from the paramagnetic to a 3-state (Potts) phase is found to be very weakly first order with behavior suggesting tricriticality at zero field. In addition to clarifying some long-standing ambiguity concerning the nature of this Potts-like transition, the present work also serves to further our understanding of the critical behavior at $T_N$, about which there has been much controversy.Comment: 10 pages (RevTex 3.0), 4 figures available upon request, CRPS-93-0

Histogram Monte Carlo study of next-nearest-neighbor Ising antiferromagnet on a stacked triangular lattice

Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the xy universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.Comment: 13 pages (RevTex 3.0), 10 figures available upon request, CRPS-93-0