TY - JOUR

T1 - Local magnetization in the boundary Ising chain at finite temperature

AU - Sela, Eran

AU - Mitchell, Andrew K.

PY - 2012/4

Y1 - 2012/4

N2 - We study the local magnetization in the 2D 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 β. This model is equivalent to the semi-infinite quantum critical 1D transverse field Ising model at temperature , with a symmetry-breaking field proportional to 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. The validity of our result as the continuum limit of the 1D lattice model is confirmed numerically, exploiting a modified Jordan-Wigner representation. Applications of the result are discussed.

AB - We study the local magnetization in the 2D 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 β. This model is equivalent to the semi-infinite quantum critical 1D transverse field Ising model at temperature , with a symmetry-breaking field proportional to 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. The validity of our result as the continuum limit of the 1D lattice model is confirmed numerically, exploiting a modified Jordan-Wigner representation. Applications of the result are discussed.

KW - conformal field theory

KW - ladders and planes (theory)

KW - renormalization group

KW - spin chains

KW - surface effects (theory)

UR - http://www.scopus.com/inward/record.url?scp=84859796826&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2012/04/P04006

DO - 10.1088/1742-5468/2012/04/P04006

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AN - SCOPUS:84859796826

SN - 1742-5468

VL - 2012

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 4

M1 - P04006

ER -