Critical behavior of the two-dimensional<i>N</i>-component Landau-Ginzburg Hamiltonian with cubic anisotropy

Calabrese, Pasquale; Celi, Alessio

doi:10.1103/physrevb.66.184410

Cited by 19 publications

(52 citation statements)

References 117 publications

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“…[22] It then follows by continuity that the thermal disordering of the DDW phase is in the KT universality class for all 0 < t < t c . For t > t c (v < 0) we also expect a KT transition in the vicinity of t c assuming that the renormalization group (RG) flows are still governed by the XY-point; however it is possible that the system will follow RG flows directed towards the fixed line existing between the XY and the Cubic fixed point [23] and that the KT-transition will change into a line of transitions with continuously varying exponents. On further increasing t this line might terminate and become first order consistent with the fluctuation-driven first order transitions known to exist in the n-vector model.…”

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confidence: 99%

Resonating Plaquette Phase of a Quantum Six-Vertex Model

Syljuåsen

Chakravarty

2006

Phys. Rev. Lett.

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The simplest quantum generalization of the six-vertex model describes fluctuations of the order parameter of the d-density wave (DDW), believed to compete with superconductivity in the highTc superconductors. The ground state of this model undergoes a first order transition from the DDW phase to a resonating plaquette phase as the quantum fluctuations are increased, which is explored with the help of quantum Monte Carlo simulations and analytic considerations involving the n-vector (n = 2) model with cubic anisotropy. In addition to finding a new quantum state, we show that the DDW is robust against a class of quantum fluctuations of its order parameter. The inferred finite temperature phase diagram contains unsuspected multicritical points.PACS numbers: 71.10.Hf, 74.10.+v The vertex models have unusual building blocks: arrows joined at a site forming the vertex. Nonetheless the statistical mechanics of these models are well defined, elegant, and have unexpected connections to more intuitively familiar models. For example, the transfer matrix of the classical six-vertex model is the XXZHamiltonian [1] of Heisenberg spins and the corresponding transfer matrix of the eight vertex model is the XYZHamiltonian.[2] Both of these models are solved by powerful mathematical methods with far reaching consequences. These vertex models are not simply products of mathematical imagination but were originally proposed to describe phases of ferro and antiferroelectric materials.[3] Thus they are effective descriptions of complex organization of matter. These vertex models are classical because they are made out of commuting variables.The interest in the quantum six-vertex model, to be defined below, is rooted in the unusual phenomenology of the cuprate high temperature superconductors.[4] It has been argued that the origin of the pseudogap is an unconventional broken symmetry in which a particle and a hole is bound in an angular momentum l = 2 state, resulting in an order parameter, the d-density wave (DDW), which is effectively hidden.[5] The statistical mechanical description of DDW, which includes both thermal and quantum fluctuations of the directions of the bond currents, is the quantum six-vertex model. [4] In particular, the description of DDW in terms of the six-vertex model resolves the puzzle as to why there are no associated specific heat anomalies, as the phase transition corresponds to an essential singularity in the free energy. In this Letter we consider commensurate DDW as possible incommensuration wave vectors tend to be small in extended Hubbard models. [6] Among the observed broken symmetries in the particleparticle channel are s, p, and d-wave superconductors, where the Cooper pairs bind in the angular momentum channels l = 0, 1, and 2 respectively. It is remarkable however, that in the particle-hole channel, the observed broken symmetries are mainly confined to s-wave symmetry: s-wave singlet and triplet density waves, known as the charge and spin density waves respectively. [7] Here we investigate, for...

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Resonating Plaquette Phase of a Quantum Six-Vertex Model

Syljuåsen

Chakravarty

2006

Phys. Rev. Lett.

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“…The mappings, in particular regions of the phase diagram, with the N-color Ashkin-Teller models, discrete cubic models, and planar model with fourth order anisotropy give further information about the critical behavior. All these issues are reviewed in [3] and we will not repeat here. These features make the 2D N-vector cubic model a convenient and, perhaps, unique testbed for evaluation of the analytical and numerical power of perturbative methods widely used nowadays in the theory of critical phenomena.…”

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confidence: 99%

“…The two-dimensional (2D) model with N-vector order parameter and cubic anisotropy is known to have a rich phase diagram; it contains, under different values of N and of the anisotropy parameter, the Ising-like and Kosterlitz-Thouless critical points, lines of the first-order phase transitions, and the line of the second-order transitions with continuously varying critical exponents (see, e. g. [1][2][3] …”

Section: Introductionmentioning

confidence: 99%

Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

Calabrese¹,

Орлов²,

Pakhnin³

et al. 2005

Condens. Matter Phys.

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The critical behavior of the two-dimensional N -vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The β functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Padé-Borel-Leroy and conformal mapping techniques. It is found that for N = 2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both β functions closer to each other. For N 3 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N = 0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.

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Section: Introductionmentioning

confidence: 99%

“…For instance, the random N-color quantum ATM can be described by an O(N ) Gross-Neveu model with random mass [16]. Similarly the relation between the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy and N-color ATM has been discussed in [17,18].Critical properties of the ATM has been widely investigated in literature. IATM has been investigated by mean field renormalization group technique [19,20], Monte Carlo Simulation (MC) [21,22,23,24,25,26,27], effective field theory (EFT) [28], transfer-matrix finite-size-scaling method [29], high and low temperature series expansion and MC [30], MC and renormalization group technique [31,32] and damage spreading simulation [33,34,35].…”

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confidence: 99%

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

Akıncı

2017

Physica A: Statistical Mechanics and its Applications

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Dynamic behavior of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analyzed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice.After defining the possible dynamical phases of the system, phase diagrams have been given and the behavior of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of this loop in different dynamical phases have been given.Keywords: Dynamic isotropic Ashkin-Teller model; hysteresis loops; hysteresis loop area IntroductionAshkin-Teller Model (ATM) has been introduced for description of the cooperative phenomena of quaternary alloys [1]. It has four states per site and may be useful to describe magnetic systems with two easy axes. The ATM is a staggered version of the eight-vertex model [2]. In two dimension, the ATM can be mapped onto a staggered eight-vertex model at the critical point. The nonuniversal critical behavior along a self-dual line, where the exponents vary continuously [3], is one of the interesting critical property of the model. On the other hand it has been shown that, three dimensional model has much richer phase diagrams than the ATM in two dimension [4]. There appear some first-order phase transitions and continuous phase transitions, even an XY -like transition and a Heisenberg-like multicritical point.It has been shown that ATM could be described in Hamiltonian form appropriate for spin systems [5]. In this form, the model can be viewed as two coupled Ising models which is named as 2-color ATM. If two of these Ising models are identical then the model named as isotropic AshkinTeller model (IATM), otherwise the model is anisotropic Ashkin-Teller model (AATM). In a similar manner, ATM that formed by N coupled Isig model entitled as N-color ATM as introduced in [6].One of the well known physical realizations for this model is the compound of Selenium adsorbed on a Ni surface [7]. ATM can be used to describe chemical interactions in metallic alloys [8], thermodynamic properties in superconducting cuprates (ATM represents the interactions between orbital current loops in CuO 2 -plaquettes) [9] and elastic response of DNA molecule to external force and torque [10]. Besides, oxygen ordering in Y Ba 2 Cu 3 O z may also be understood in analogy with the two-dimensional IATM [11,12,13]. Also, ATM has many interesting applications in neural networks [14] and cosmology [15]. Besides, some mappings between the ATM and some other models are possible. This makes the ATM valuable in a theoretical manner. For instance, the random N-color quantum ATM can be described by an O(N ) Gross-Neveu model with random mass [16]. Similarly the relation between the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy and N-color ATM has been discussed in [17,18].Criti...

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Critical behavior of the two-dimensionalN-component Landau-Ginzburg Hamiltonian with cubic anisotropy

Cited by 19 publications

References 117 publications

Resonating Plaquette Phase of a Quantum Six-Vertex Model

Resonating Plaquette Phase of a Quantum Six-Vertex Model

Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

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