Local magnetization in the boundary Ising chain at finite temperature

Eran Sela*, Andrew K. Mitchell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numberP04006
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
StatePublished - Apr 2012
Externally publishedYes


  • conformal field theory
  • ladders and planes (theory)
  • renormalization group
  • spin chains
  • surface effects (theory)


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