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Bootstrapping the Ising Model on the Lattice
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We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous two-sided bounds on spin correlators through semi-definite programming. For the 2D Ising model on the square lattice, the bootstrap bounds based on correlators supported in a 13-site diamond-shaped region determine the nearest-spin correlator to within a small window, which for a wide range of coupling and magnetic field is narrower than the precision attainable with Monte Carlo methods. We also report preliminary results of the bootstrap bounds for the 3D Ising model on the cubic lattice.
Forward citations
Cited by 3 Pith papers
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The Bootstrap of Points and Lines
A mixed-correlator bootstrap for 2D boundary CFTs produces new rigorous bounds on boundary entropy, bulk-to-boundary OPE coefficients, and gap spectra, tested on Ising and free boson and applied to su(2)_2 WZW.
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Bootstrapping Euclidean Two-point Correlators
A semidefinite programming bootstrap is formulated for Euclidean two-point correlators in quantum mechanics, yielding rigorous bounds and low-lying spectrum extraction in the ungauged one-matrix model.
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Bootstrapping periodic quantum systems
A bootstrap method that includes the translation operator and uses reality conditions computes accurate Bloch-band dispersion relations for the cosine potential without positivity constraints.
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