245 research outputs found

    Correlation Functions Along a Massless Flow

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    A non-perturbative method based on the Form Factor bootstrap approach is proposed for the analysis of correlation functions of 2-D massless integrable theories and applied to the massless flow between the Tricritical and the Critical Ising Models.Comment: 11 pages (two figures not included in the text), Latex file, ISAS/EP/94/15

    On Perturbations of Unitary Minimal Models by Boundary Condition Changing Operators

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    In this note we consider boundary perturbations in the A-Series unitary minimal models by phi_{r,r+2} fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example phi_{1,3} and find that this sheds light on more general phi_{r,r+2} perturbations. Finally, we find a simple diagrammatic representation for the space of flows from a single Cardy boundary condition.Comment: 27 pages, 10 figure

    Conformal Field Theory and Hyperbolic Geometry

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    We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully factored form for the three-point function. A doubly-infinite discrete series of central charges with limit c=-2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges. Note: email after 12/19: [email protected]: 7 pages (PlainTeX

    Comment on "Phase Diagram of an Asymmetric Spin Ladder."

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    A comment to the paper by S. Chen, H. B\"uttner, and J. Voit, [Phys. Rev. Lett. {\bf 87}, 087205 (2001)].Comment: 1 page, 1 figure, to appear in Physical Review Letter

    Asymptotic factorisation of form factors in two-dimensional quantum field theory

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    It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the form factor bootstrap approach. A sum rule which yields the scaling dimension of such operators is also derived.Comment: 11 pages, late

    Strong Conformal Dynamics at the LHC and on the Lattice

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    Conformal technicolor is a paradigm for new physics at LHC that may solve the problems of strong electroweak symmetry breaking for quark masses and precision electroweak data. We give explicit examples of conformal technicolor theories based on a QCD-like sector. We suggest a practical method to test the conformal dynamics of these theories on the lattice.Comment: v2: Generalized discussion of lattice measurement of hadron masses, references added, minor clarifications v3: references added, minor change

    Free boson formulation of boundary states in W_3 minimal models and the critical Potts model

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    We develop a Coulomb gas formalism for boundary conformal field theory having a WW symmetry and illustrate its operation using the three state Potts model. We find that there are free-field representations for six WW conserving boundary states, which yield the fixed and mixed physical boundary conditions, and two WW violating boundary states which yield the free and new boundary conditions. Other WW violating boundary states can be constructed but they decouple from the rest of the theory. Thus we have a complete free-field realization of the known boundary states of the three state Potts model. We then use the formalism to calculate boundary correlation functions in various cases. We find that the conformal blocks arising when the two point function of ϕ2,3\phi_{2,3} is calculated in the presence of free and new boundary conditions are indeed the last two solutions of the sixth order differential equation generated by the singular vector.Comment: 25 page

    Open-closed field algebras

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    We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde

    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 Knn≄0K_{\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, H≠0H\neq 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H→∞H \to \infty this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential

    Reaction-controlled diffusion: Monte Carlo simulations

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    We study the coupled two-species non-equilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may independently hop to an adjacent lattice site provided it is occupied by at least one B particle. The B particle species undergoes diffusion-limited reactions. In an active state with nonzero, essentially homogeneous B particle saturation density, the A species displays normal diffusion. In an inactive, absorbing phase with exponentially decaying B density, the A particles become localized. In situations with algebraic decay rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous phase transition separating active and absorbing states, or in a power-law inactive phase, the A particles propagate subdiffusively with mean-square displacement ~ t^{1-alpha_A}. We find that within the accuracy of our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field approach. This remains true even in the presence of strong spatio-temporal fluctuations of the B density. However, in contrast with the mean-field results, our data yield a distinctly non-Gaussian A particle displacement distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar for the different processes investigated here. Fluctuations of effective diffusion rates cause a marked enhancement of n_A(x,t) at low displacements |x|, indicating a considerable fraction of practically localized A particles, as well as at large traversed distances.Comment: Revtex, 19 pages, 27 eps figures include