3,158 research outputs found

    Determinant of the Potts model transfer matrix and the critical point

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    By using a decomposition of the transfer matrix of the qq-state Potts Model on a three dimensional m×n×n m \times n \times n simple cubic lattice its determinant is calculated exactly. By using the calculated determinants a formula is conjectured which approximates the critical temperature for a d-dimensional hypercubic lattice.Comment: 8 page

    Quantum Group Representations and Baxter Equation

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    In this paper we propose algebraic universal procedure for deriving "fusion rules" and Baxter equation for any integrable model with Uq(sl^2)U_q(\widehat{sl}_2) symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is got from the certain infinite dimensional representation called q-oscillator one of the Universal R- matrix for Uq(sl^2)U_q(\widehat{sl}_2) affine algebra (first proposed by V. Bazhanov, S.Lukyanov and A.Zamolodchikov for quantum KdV case). We also examine the algebraic properties of Q-operator.Comment: 14 pages, Latex file, corrected references and acknowledgment

    The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

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    We study the Ising model on the triangular lattice with nearest-neighbor couplings KnnK_{\rm nn}, next-nearest-neighbor couplings Knnn>0K_{\rm nnn}>0, and a magnetic field HH. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case Knn<0K_{\rm nn}<0, but we also explore the ferromagnetic regime Knn0K_{\rm nn}\ge 0 for H=0. For Knn<0K_{\rm nn}<0 and H=0 we locate a critical phase presumably covering the whole range <Knn<0-\infty < K_{\rm nn}<0. For Knn<0K_{\rm nn}<0, H0H\neq 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit HH \to \infty this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential

    Exact expectation values of local fields in quantum sine-Gordon model

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    We propose an explicit expression for vacuum expectation values of the exponential fields in the sine-Gordon model. Our expression agrees both with semi-classical results in the sine-Gordon theory and with perturbative calculations in the Massive Thirring model. We use this expression to make new predictions about the large-distance asymptotic form of the two-point correlation function in the XXZ spin chain.Comment: 18 pages, harvmac.tex, 2 figure

    The elliptic gamma function and SL(3,Z) x Z^3

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    The elliptic gamma function is a generalization of the Euler gamma function and is associated to an elliptic curve. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma function, respectively. The elliptic gamma function appears in Baxter's formula for the free energy of the eight-vertex model and in the hypergeometric solutions of the elliptic qKZB equations. In this paper, the properties of this function are studied. In particular we show that elliptic gamma functions are generalizations of automorphic forms of G=SL(3,Z) x Z^3 associated to a non-trivial class in H^3(G,Z).Comment: 27 pages, LaTeX References added, minor correction

    Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)E_{\tau,\eta}(sl_2)

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    To each representation of the elliptic quantum group Eτ,η(sl2)E_{\tau,\eta}(sl_2) is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method. Special cases of this construction give eigenvectors for IRF models, for the eight-vertex model and for the two-body Ruijsenaars operator. The latter is a qq-deformation of Hermite's solution of the Lam\'e equation.Comment: 18 pages, AMSLaTe

    Integrable Quantum Field Theories in Finite Volume: Excited State Energies

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    We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate compactified on a circle of circumference R. The IQFT ``commuting transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator Φ1,3\Phi_{1,3}. We study the models in which the fusion relations for these ``transfer-matrices'' truncate and provide closed integral equations which generalize the equations of Thermodynamic Bethe Ansatz to excited states. The explicit calculations are done for the first excited state in the ``Scaling Lee-Yang Model''.Comment: 54 pages, harvmac, epsf, TeX file and postscript figures packed in a single selfextracting uufile. Compiles only in the `Big' mode with harvma

    Yang-Baxter maps and symmetries of integrable equations on quad-graphs

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    A connection between the Yang-Baxter relation for maps and the multi-dimensional consistency property of integrable equations on quad-graphs is investigated. The approach is based on the symmetry analysis of the corresponding equations. It is shown that the Yang-Baxter variables can be chosen as invariants of the multi-parameter symmetry groups of the equations. We use the classification results by Adler, Bobenko and Suris to demonstrate this method. Some new examples of Yang-Baxter maps are derived in this way from multi-field integrable equations.Comment: 20 pages, 5 figure

    Dynamics of the 2d Potts model phase transition

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    The dynamics of 2d Potts models, which are temperature driven through the phase transition using updating procedures in the Glauber universality class, is investigated. We present calculations of the hysteresis for the (internal) energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used to define finite volume estimators of physical observables, which can be used to study the approach to the infinite volume limit. We compare with equilibrium configurations and the preliminary indications are that the dynamics leads to considerable alterations of the statistical properties of the configurations studied.Comment: Lattice2002(spin
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