Local magnetization in the boundary Ising chain at finite temperature

Abstract

We study the local magnetization in the 2D Ising model at its critical temperatureon a semi-infinite cylinder geometry, and with a nonzero magnetic fieldh applied at the circular boundary of circumferenceβ. This model is equivalent to the semi-infinite quantum critical 1D transverse field Isingmodel at temperature , with a symmetry-breaking field proportional toh applied at the point boundary. Using conformal field theory methods we obtain the fullscaling function for the local magnetization analytically in the continuum limit, therebyrefining the previous results of Leclair, Lesage and Saleur. The validity of ourresult as the continuum limit of the 1D lattice model is confirmed numerically,exploiting a modified Jordan–Wigner representation. Applications of the result arediscussed.