Conformal Profiles in the Hilhorst--van Leeuwen Model

Abstract

We study the critical energy and magnetization profiles for the Ising quantum chain with a marginal extended surface perturbation of the form A/y, y being the distance from the surface (Hilhorst-van Leeuwen model). For weak local couplings, A<A_c, the model displays a continuous surface transition with A-dependent exponents, whereas, for A>A_c, there is surface order at the bulk critical point. If conformal invariance is assumed to hold with such marginal perturbations, it predicts conformal profiles with the same scaling form as for the unperturbed quantum chain, with marginal surface exponents replacing the unperturbed ones. The results of direct analytical and numerical calculations of the profiles confirm the validity of the conformal expressions in the regimes of second- and first-order surface transitions.

arXiv comment12 pages, 4 figures, TeX, IOP macros included

References in corpus (6)

• Inhomogeneous Systems with Unusual Critical Behaviour
• Conformal invariance and linear defects in the two-dimensional Ising model
• Marginal Anisotropy in Layered Aperiodic Ising Systems
• Radial marginal perturbation of two-dimensional systems and conformal invariance
• Off-Diagonal Density Profiles and Conformal Invariance
• Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations

Cited by in corpus (7)

• Quantum Ising chains with boundary fields
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• The density of critical percolation clusters touching the boundaries of strips and squares
• Density of critical clusters in strips of strongly disordered systems
• Conformal off-diagonal boundary density profiles on a semi-infinite strip
• Iterated star-triangle transformation on inhomogeneous 2D Ising lattices
• Multiscaling in Ising quantum chains with random Hilhorst-van Leeuwen perturbations