Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

Abstract

We study the finite-temperature behaviour of two-dimensional S = 1/2 Heisenberg antiferromagnets with very weak easy-axis and easy-plane exchange anisotropies. By means of quantum Monte Carlo simulations, based on the continuous-time loop and worm algorithm, we obtain a rich set of data that allows us to draw conclusions about both the existence and the type of finite-temperature transition expected in the considered models. We observe that the essential features of the Ising universality class, as well as those of the Berezinskii-Kosterlitz-Thouless (BKT) one, are preserved even for anisotropies as small as 10 −3 times the exchange integral; such outcome, being referred to the most quantum case S = 1/2, rules out the possibility for quantum fluctuations to destroy the long or quasi-long range order, whose onset is responsible for the Ising or BKT transition, no matter how small the anisotropy. Besides this general issue, we use our results to extract, out of the isotropic component, the features which are peculiar to weakly anisotropic models, with particular attention for the temperature region immediately above the transition. By this analysis we aim to give a handy tool for understanding the experimental data relative to those real compounds whose anisotropies are too weak for a qualitative description to accomplish the goal of singling out the genuinely two-dimensional critical behaviour.

Importance of In-Plane Anisotropy in the Quasi-Two-Dimensional AntiferromagnetBaNi2V2O8

“…Further, the search for a magnetic system exhibiting true Berezinskii-Kosterlitz-Thouless (BKT) behavior, initially proposed for 2D XY magnetic systems [2], has been elusive and has only been seen in superfluid and superconducting films [3]. Theoretical studies indicate that BKT behavior can also be expected for 2D Heisenberg systems with a small easy-plane XY anisotropy [4]. Two recent experimental papers suggest that BaNi 2 V 2 O 8 may in fact be a physical realization of such a system [5,6].…”

“…(1), a true BKT transition could be expected within each 2D layer [4]. However, a real crystal is always three-dimensional (3D) and a very small interlayer exchange J ′ ultimately leads to a crossover from 2D to 3D correlations, and then to a 3D ordering transition [4].…”

“…Our analysis and comparison with literature indicates that the obtained (T, H) phase diagram may be generic to quasi 2D antiferromagnets with a degenerate number of easy axes and with J ≫ D XY ≫ D IP , J ′ . It would be useful if the theoretical models for quasi-2D Heisenberg systems, which already consider XY anisotropy and interplane coupling [4], would also incorporate this in-plane anisotropy.Single crystals of BaNi 2 V 2 O 8 (42.8 mg) and BaNi 0.8 Mg 1.2 V 2 O 8 (4.85 mg) were grown in fluxes composed of BaCO 3 , NiO, MgO, and V 2 O 5 , using Al 2 0 3 crucibles. Specific heat was measured using a PPMS from Quantum Design [9].…”

“…Our analysis and comparison with literature indicates that the obtained (T, H) phase diagram may be generic to quasi 2D antiferromagnets with a degenerate number of easy axes and with J ≫ D XY ≫ D IP , J ′ . It would be useful if the theoretical models for quasi-2D Heisenberg systems, which already consider XY anisotropy and interplane coupling [4], would also incorporate this in-plane anisotropy.…”

Finite Size Scaling, Fisher Zeroes and Super Yang-Mills

“…Following the Quantum Monte Carlo improvedestimator definitions for conventional thermodynamic (2nd derivative of free energy) observables [7] such as the uniform χ u and the second moment definition of correlation length ξ 2 , we introduce a Fisher zeros improved-estimator polynomial expansion in the coupling J ab to determine independently the FSS properties of α c . We plot the Fisher zeros in the complex J 2 ab plane in Fig.4, noting the pinching of the real axis corresponding to the discontinuities in the partition function that in the thermodynamic limit give α c .…”