Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations

Abstract

The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which exact results have been previously obtained. The first-order corrections to the local exponents, which are functions of the amplitude of the defect, are deduced from a perturbation expansion of the two-point correlation functions. Assuming covariance under conformal transformation, the perturbed system is mapped onto a cylinder. Working in the Hamiltonian limit, the first-order corrections to the lowest gaps are calculated for the Ising model. The results confirm the validity of the gap-exponent relations for the perturbed system.

11 pages, Plain TeX, epsf

References in corpus (2)

• Conformal invariance and linear defects in the two-dimensional Ising model
• Radial marginal perturbation of two-dimensional systems and conformal invariance

Cited by in corpus (5)

• Inhomogeneous Systems with Unusual Critical Behaviour
• Conformal Profiles in the Hilhorst--van Leeuwen Model
• Realization of supersymmetric quantum mechanics in inhomogeneous Ising models
• Introduction to thermodynamics of spin models in the Hamiltonian limit
• Multiscaling in Ising quantum chains with random Hilhorst-van Leeuwen perturbations