Short distance behaviour of correlators in the 2D Ising model in a magnetic field

Abstract

We study the spin-spin, spin-energy and energy-energy correlators in the 2d Ising model perturbed by a magnetic field. We compare the results of a set of high precision Montecarlo simulations with the predictions of two different approximations: the Form Factor approach, based on the exact S-matrix description of the model, and a short distance perturbative expansion around the conformal point. Both methods give very good results, the first one performs better for distances larger than the correlation length, while the second one is more precise for distances smaller than the correlation length. In order to improve this agreement we extend the perturbative analysis to the second order in the derivatives of the OPE constants.

arXiv comment46 pages, 10 figures, final version to appear in Nucl. Phys. B

References in corpus (11)

• Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Universal Properties of Self-Avoiding Walks from Two-Dimensional Field Theory
• Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$
• All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator
• Lattice Ising model in a field: E${}_8$ scattering theory
• Vacuum Expectation Values from a variational approach
• Composite Operators in QCD
• On the Short Distance Behavior of the Critical Ising Model Perturbed by a Magnetic Field
• Scaling Limit of the Ising Model in a Field
• Manifestly Finite Perturbation Theory for the Short-Distance Expansion of Correlation Functions in the Two Dimensional Ising Model

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• Tethered Monte Carlo: computing the effective potential without critical slowing down
• Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field
• Conformal perturbation theory
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• Study of the 2d Ising Model with mixed perturbation
• Conformal perturbation of off-critical correlators in the 3D Ising universality class
• Potts correlators and the static three-quark potential
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase
• Finite temperature corrections in 2d integrable models
• On the third level descendent fields in the Bullough-Dodd model and its reductions
• A new class of short distance universal amplitude ratios
• Fundamental Matter and the Deconfining Phase Transition in 2+1 D