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Ward Identities and Integrable Differential Equations in the Ising Field Theory

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arxiv hep-th/0309228 v1 pith:ZFKC73DO submitted 2003-09-25 hep-th cond-mat

P. Fonseca , A. Zamolodchikov This is my paper
classification hep-thcond-mat
keywords fieldisingequationsidentitiestheorywardsigmaapplied
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We show that the celebrated Painleve equations for the Ising correlation functions follow in a simple way from the Ward Identities associated with local Integrals of Motion of the doubled Ising field theory. We use these Ward Identities to derive the equations determining the matrix elements of the product $\sigma(x)\sigma(x')$ between any particle states. The result is then applied in evaluating the leading mass corrections in the Ising field theory perturbed by an external magnetic field.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising the way into de Sitter

    hep-th 2026-07 conditional novelty 8.0 of 10

    The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.

  2. Real-time Scattering in \phi^4 Theory using Matrix Product States

    hep-th 2025-11 unverdicted novelty 7.0 of 10

    uMPS simulations of φ⁴ theory in 1+1 dimensions extract elastic scattering probabilities and time delays that diverge near the critical point, serving as a dynamical signature of the quantum phase transition.

  3. Meson mass spectrum in Ising Field Theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    The authors derive exact spectral sums and WKB expansions for Bethe-Salpeter meson masses in Ising field theory and predict meson mass degeneracies at complex critical points.

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