1,325 research outputs found

    Off-critical correlations in the Ashkin-Teller model

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    We use the exact scattering description of the scaling Ashkin-Teller model in two dimensions to compute the two-particle form factors of the relevant operators. These provide an approximation for the correlation functions whose accuracy is tested against exact sum rules.Comment: 8 pages, late

    Universal Ratios and Correlation Functions

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    We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of disorder operators in a free theory of complex bosonic and fermionic field, correlators ruled by a Painleve differential equation.Comment: 10 pages, JHEP Proceedings of the Workshop on Integrable Theories, Solitons and Duality, IFT-Unesp, Sao Paulo, Brasi

    Correlators in integrable quantum field theory. The scaling RSOS models

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    The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in terms of colliding particles, we compute the correlation functions of the thermal, ϕ1,2\phi_{1,2} and (for some cases) spin operators in the two-particle approximation. The accuracy obtained for the moments of these correlators is analysed by computing the central charge and the scaling dimensions and comparing with the exact results. We further consider the (generally non-integrable) perturbation of the critical points with both the operators ϕ1,3\phi_{1,3} and ϕ1,2\phi_{1,2} and locate the branches solved on the lattice within the associated two-dimensional phase diagram. Finally we discuss the fact that the RSOS models, the dilute qq-state Potts model at and the O(n) vector model are all described by the same perturbed conformal field theory.Comment: 22 pages, late

    The Field Theory of the q->4+ Potts Model

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    The q-state Potts model in two dimensions exhibits a first-order transition for q>4. As q->4+ the correlation length at this transition diverges. We argue that this limit defines a massive integrable quantum field theory whose lowest excitations are kinks connecting 4+1 degenerate ground states. We construct the S-matrix of this theory and the two-particle form factors, and hence estimate a number of universal amplitude ratios. These are in very good agreement with the results of extrapolated series in q^(-1/2) as well as Monte Carlo results for q=5.Comment: 8 pages, 1 figure; late

    Field theory of scaling lattice models. The Potts antiferromagnet

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    In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T->0 is argued to be described exactly by the sine-Gordon field theory at a specific value of the coupling. The solution of the scaling ferromagnetic case is recalled for comparison. The field theory describing the crossover from antiferromagnetic to ferromagnetic behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200

    Susceptibility amplitude ratios in the two-dimensional Potts model and percolation

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    The high-temperature susceptibility of the qq-state Potts model behaves as ΓTTcγ\Gamma|T-T_c|^{-\gamma} as TTc+T\to T_c+, while for TTcT\to T_c- one may define both longitudinal and transverse susceptibilities, with the same power law but different amplitudes ΓL\Gamma_L and ΓT\Gamma_T. We extend a previous analytic calculation of the universal ratio Γ/ΓL\Gamma/\Gamma_L in two dimensions to the low-temperature ratio ΓT/ΓL\Gamma_T/\Gamma_L, and test both predictions with Monte Carlo simulations for q=3q=3 and 4. The data for q=4q=4 are inconclusive owing to large corrections to scaling, while for q=3q=3 they appear consistent with the prediction for ΓT/ΓL\Gamma_T/\Gamma_L, but not with that for Γ/ΓL\Gamma/\Gamma_L. A simple extrapolation of our analytic results to q1q\to1 indicates a similar discrepancy with the corresponding measured quantities in percolation. We point out that stronger assumptions were made in the derivation of the ratio Γ/ΓL\Gamma/\Gamma_L, and our work suggests that these may be unjustified.Comment: 17 pages, late

    Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at T=TcT=T_c

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    The one and two-particle form factors of the energy operator in the two-dimensional Ising model in a magnetic field at T=TcT=T_c are exactly computed within the form factor bootstrap approach. Together with the matrix elements of the magnetisation operator already computed in ref.\,\cite{immf}, they are used to write down the large distance expansion for the correlators of the two relevant fields of the model.Comment: 18 pages, latex, 7 table

    First order phase transitions and integrable field theory. The dilute q-state Potts model

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    We consider the two-dimensional dilute q-state Potts model on its first order phase transition surface for 0<q\leq 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of the dilution, thermal and spin operators. They provide an approximation for the correlation functions whose accuracy is illustrated by evaluating the central charge and the scaling dimensions along the tricritical line.Comment: 21 pages, late
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