Monte Carlo study of the Heisenberg antiferromagnet on the triangular lattice

Southern, B. W.; Xu, HJ

doi:10.1103/physrevb.52.r3836

Cited by 41 publications

(55 citation statements)

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“…The critical behavior of the Heisenberg frustrated antiferromagnet is clearer; many experiments [31] agree with theoretical predictions based on topological considerations [32][33][34], Monte Carlo simulations [32,33,[35][36][37][38]27], the application of appropriate N Lσ models [39][40][41][42][43] and by the use of ERG [44]. The order parameter space of this model is the group of 3D rotations, in fact O(3)/Z 2 ≡ SO(3) ≡ P 3 [32].…”

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confidence: 54%

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Critical behavior of two-dimensional frustrated spin models with noncollinear order

Calabrese

Parruccini

2001

Phys. Rev. B

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We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this purpose we consider the corresponding O(N ) × O(2) Landau-Ginzburg-Wilson (LGW) Hamiltonian and compute the field-theoretic expansion to four loops and determine its large-order behavior. We show the existence of a stable fixed point for the physically relevant cases of two-and threecomponent spin models. We also give a prediction for the critical exponent η which is η = 0.24(6) and η = 0.29(5) for N = 3 and 2 respectively.

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confidence: 54%

“…Exact values do not exist for the Heisenberg frustrated model. The result of a very recent and accurate Monte Carlo simulation [38] is σ ∼ 0.600, even if the standard KT form of thermodynamic quantities has been used in the past to fit Monte Carlo data finding a reasonable agreement [33,37,36].…”

Section: Frustrated Heisenberg Modelmentioning

confidence: 99%

Critical behavior of two-dimensional frustrated spin models with noncollinear order

Calabrese

Parruccini

2001

Phys. Rev. B

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“…Arguments involving entropy and energy of the defects suggest the occurence of a change of behavior at a finite temperature T V between a pure spin-wave regime with confined vortices for T < T V and a regime of free vortices for T > T V . Several Monte Carlo studies of the HAFT model [8][9][10][11] and of some generalizations with an easy-axis exchange anisotropy [12][13][14] have indeed revealed the existence of various regimes resulting from the presence of defects. Here, our purpose is to shed some light on the interplay between vortices and spin-waves in 2D by studying with Monte Carlo simulations two lattice models of ferromagnetically interacting tops.…”

Section: Introductionmentioning

confidence: 99%

Spin stiffness and topological defects in two-dimensional frustrated spin systems

et al. 2001

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Using a collective Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.

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“…The predicted lowtemperature phase is an exotic spin-liquid phase where the two-point spin correlation decays exponentially and the spin correlation length remains finite. A quantity called vorticity modulus, characterizing such exotic vortex order not accompanying the conventional spin order, was proposed and calculated [58,59].…”

Section: (B) Helimagnetsmentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

342

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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Monte Carlo study of the Heisenberg antiferromagnet on the triangular lattice

Cited by 41 publications

References 1 publication

Critical behavior of two-dimensional frustrated spin models with noncollinear order

Critical behavior of two-dimensional frustrated spin models with noncollinear order

Spin stiffness and topological defects in two-dimensional frustrated spin systems

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