Evidence for a bicritical point in theXXZHeisenberg antiferromagnet on a simple cubic lattice

Abstract

The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy, the XXZ model, in a magnetic field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. Analyzing, especially, various staggered susceptibilities and Binder cumulants, we present clear evidence for the meeting point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions based on various theoretical approaches.PACS numbers: 75.10. Hk, 75.40.Cx, 05.10.Ln Uniaxially anisotropic Heisenberg antiferromagnets in a magnetic field have been studied quite extensively in the past, both experimentally and theoretically [1,2]. Usually, they display, at low temperatures and fields, the antiferromagnetic phase and, when increasing the field, the spin-flop phase. A prototypical model describing these phases as well as, possibly, multicritical points, is the Heisenberg model with a uniaxial exchange anisotropy, the XXZ modelwhere, of length one at neighboring sites, i and j, on a simple cubic lattice, ∆ is the uniaxial exchange anisotropy, 1 > ∆ > 0, and H is the applied magnetic field along the easy axis, the z-axis. The phase diagram of the model has been investigated already several years ago, using, among others, mean-field theory [3], Monte Carlo (MC) simulations [4], and high temperature series expansions [5]. The transition between the antiferromagnetic (AF) and spin-flop (SF) phases seems to be of first order, while the boundaries of the paramagnetic (P) phase to the AF and SF phases are believed to be continuous transitions in the Ising and XY universality classes, respectively. Moreover, based on renormalization group analyses in one-loop-order, a bicritical point in the Heisenberg universality class had been proposed, at which the three different phases meet [6,7]. This scenario has been questioned on the basis of renormalization group calculations in high-loop-order [8], where the bicritical point has been argued to be unstable against a tetracritical point [9], which, in turn, may be unstable towards transitions of first order in the vicinity of the meeting point of the three phases. However, a subsequent renormalization group analysis in two-loop-order [10] suggests that a bicritical point in the Heisenberg universality class can not be excluded.As has been noted quite recently [11], not only AF and SF phases, but also biconical (BC) structures [7] may play an important role in the XXZ model. Indeed, such BC structures are degenerate ground states at the critical field separating AF and SF configurations at zero temperature. For the XXZ model on a square lattice, these degenerate BC fluctuations lead to a narrow disordered phase intervening between the AF and SF phases at low temperatures, giving, presumably, rise to a 'hidden tetracritical point' [11,12] at zero temperature. A recent Monte Carlo study [13] for the XXZ antiferromagnet on a simple cubic lattice showed that biconical structures, arising ...

Competing orders, competing anisotropies, and multicriticality: The case of Co-dopedYbRh2Si2

“…At T = 0 there is a first-order phase transition between in-plane and c-axis order at D = zJ /2, where z is the lattice coordination number. This transition continues to finite T and terminates at at bicritical point [22][23][24]. To efficiently sample all spin configurations close to this first-order phase transition, we employ the parallel-tempering algorithm [25,26].…”

High-resolution Monte Carlo study of the multicritical point in the three-dimensionalXXZHeisenberg antiferromagnet

“…The uniaxially anisotropic three-dimensional (3D) Heisenberg antiferromagnet model in an external field has attracted great interest during recent decades [1][2][3][4][5][6][7][8][9][10]. Possible experimental realizations of this model include NiCl 2 ·6H 2 O [11][12][13], MnF 2 [14][15][16], and GdAlO 3 [17][18][19], among others.…”

Bicritical or tetracritical: the 3D anisotropic Heisenberg antiferromagnet

“…1 of Ref. [17]. The multicritical point where the AF, SF, and P phases meet was determined to be [17] at k B T/J = 1.025 ± 0.0025 and H/J = 3.89 ± 0.01.…”

“…A subsequent renormalization group study in two-loop order proposes that a bicritical point in the 3D Heisenberg universality class cannot be excluded [15]. Recent Monte Carlo simulations using Metropolis sampling, focusing on simple cubic lattices with linear sizes L up to 32, and carrying out critical property analysis using finite size scaling on the multicritical point [16,17] corroborate a scenario with a bicritical point in the 3D Heisenberg universality class. However, a subsequent numerical analysis of anisotropic perturbations in three-dimensional O(N)-symmetric vector models suggests [18] that for the model in question here, the stable fixed point has a biconical structure (see Fig.…”