On the Short Distance Behavior of the Critical Ising Model Perturbed by a Magnetic Field

Abstract

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).

19 pages, LATEX, 2 figures

References in corpus (5)

• 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
• Composite Operators in QCD
• Operator Coefficients for Composite Operators in the $({\varphi }^4{)}_4$ Theory
• Manifestly Finite Perturbation Theory for the Short-Distance Expansion of Correlation Functions in the Two Dimensional Ising Model

Cited by in corpus (21)

• Integrable field theory and critical phenomena. The Ising model in a magnetic field
• Conformal perturbation theory beyond the leading order
• Universal Amplitude Ratios of The Renormalization Group: Two-Dimensional Tricritical Ising Model
• Vacuum Expectation Values from a variational approach
• Tricritical Ising Model near criticality
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Short distance behaviour of correlators in the 2D Ising model in a magnetic field
• Scaling Limit of the Ising Model in a Field
• Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field
• Quantum critical response: from conformal perturbation theory to holography
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• Expectation values of descendent fields in the Bullough-Dodd model and related perturbed conformal field theories
• OPE Coefficients of the 3D Ising model with a trapping potential
• Study of the 2d Ising Model with mixed perturbation
• Conformal perturbation of off-critical correlators in the 3D Ising universality class
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• Potts correlators and the static three-quark potential
• Liouville field theory coupled to a critical Ising model: Non-perturbative analysis, duality and applications
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• A new class of short distance universal amplitude ratios
• Energy trapped Ising model