Conformal perturbation theory

Abstract

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point one needs to know the model at the critical (conformal) point. In this line, recent progresses in the knowledge of conformal field theories, through the conformal bootstrap, give the hope to get some interesting results also outside of the critical point. In this note we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the $2D$ Ising model.

21 pages, Version to appear on PRD

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Critical Behavior of a Trapped Interacting Bose Gas
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Long-range critical exponents near the short-range crossover
• Dynamical response near quantum critical points
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

Cited by in corpus (12)

• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Note on Rényi entropy of 2D perturbed free fermions
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• Renormalization group flows in AdS and the bootstrap program
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• Renormalization group in quantum critical theories with Harris-marginal disorder
• The tricritical Ising CFT and conformal bootstrap
• Fermionic Magic Resources of Quantum Many-Body Systems
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories
• Energy trapped Ising model