Field theory of bicritical and tetracritical points. I. Statics

Folk, R.; Holovatch, Yu.; Moser, G.

doi:10.1103/physreve.78.041124

Cited by 41 publications

(109 citation statements)

References 40 publications

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“…Usual order-disorder transitions and relaxational dynamical critical behavior near critical points in a related model in higher dimensions (e.g., three dimensions) have been studied in Ref. [12], where a variety of temperature driven phase transitions separating the disordered and the ordered phases are discussed. Unlike Ref.…”

Section: Model I: Nls Coupled With Ising Spinsmentioning

confidence: 99%

Phase transitions and order in two-dimensional generalized nonlinearσmodels

2015

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We study phase transitions and the nature of order in a class of classical generalized O(N ) nonlinear σ-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between stiff and soft phases, where the effective spin stiffness, respectively, diverges and vanishes in the long wavelength limit at two dimensions (2d), unlike in pure NLS. In the stiff phase, in the thermodynamic limit the variance of the transverse spin (or, the Goldstone mode) fluctuations are found to scale with the system size L in 2d as ln ln L with a model-dependent amplitude, that is markedly weaker than the well-known ln L-dependence of the variance of the broken symmetry modes in models that display quasi-long range order in 2d. Equivalently, for N = 2 at 2d the equal-time spin-spin correlations decay in powers of inverse logarithm of the spatial separation with model-dependent exponents. These transitions are controlled by the model parameters those couple the O(N ) spins with the additional variables. In the presence of long-range noises in example (iii), true long-range order may set in 2d, depending upon the specific details of the underlying dynamics. Our results should be useful in understanding phase transitions in equilibrium and nonequilibrium low-dimensional systems with continuous symmetries in general.

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Section: Model I: Nls Coupled With Ising Spinsmentioning

confidence: 99%

Phase transitions and order in two-dimensional generalized nonlinearσmodels

2015

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“…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.…”

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confidence: 99%

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confidence: 99%

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

Selke

2011

Phys. Rev. E

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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 ...

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“…1(c)). 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.…”

Section: Introductionmentioning

confidence: 83%

Bicritical or tetracritical: the 3D anisotropic Heisenberg antiferromagnet

Tsai

Landau

2014

J. Phys.: Conf. Ser.

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Abstract.The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilities and the probability distribution of the magnetization to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

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Field theory of bicritical and tetracritical points. I. Statics

Cited by 41 publications

References 40 publications

Phase transitions and order in two-dimensional generalized nonlinearσmodels

Phase transitions and order in two-dimensional generalized nonlinearσmodels

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

Bicritical or tetracritical: the 3D anisotropic Heisenberg antiferromagnet

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