Local Magnetization in the Boundary Ising Chain at Finite Temperature

Abstract

We study the local magnetization in the 2-D Ising model at its critical temperature on a semi-infinite cylinder geometry, and with a nonzero magnetic field $h$ applied at the circular boundary of circumference $\beta$. This model is equivalent to the semi-infinite quantum critical 1-D transverse field Ising model at temperature $T\propto {\beta }^{-1}$, with a symmetry-breaking field $\propto h$ applied at the point boundary. Using conformal field theory methods we obtain the full scaling function for the local magnetization analytically in the continuum limit, thereby refining the previous results of Leclair, Lesage and Saleur in Ref. \onlinecite{Leclair}. The validity of our result as the continuum limit of the 1-D lattice model is confirmed numerically, exploiting a modified Jordan-Wigner representation. Applications of the result are discussed.

9 pages, 3 figures

References in corpus (3)

• Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud
• Exact crossover Green function in the two-channel and two-impurity Kondo models
• Dynamical response functions in the quantum Ising chain with a boundary

Cited by in corpus (6)

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• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
• Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions
• Probing single-electron scattering through a non-Fermi liquid charge-Kondo device