Correlation functions of the semi-infinite two-dimensional ising model

R. Z. Bariev

R. Z. Bariev

Bülent Kutlu, Nevzat AKTEKİN

Theodore W. Burkhardt, Ihnsouk Guim

By solving partial differential equations for the correlation functions implied by conformal invariance, we obtain exact results at the critical point for the bulk six-point function 〈\ensuremath{\sigma}(1)...\ensuremath{\sigma}(6)〉 of the two-dimensional Ising model and the three-point functions 〈\ensuremath{\sigma}(1)\ensuremath{\sigma}(2)\ensuremath{\sigma}(3)〉, 〈\ensuremath{\sigma}(1)\ensuremath{\mu}(2)\ensuremath{\mu}(3)〉 of the semi-infinite two-dimensional Ising model with fixed boundary spins. Here \ensuremath{\sigma} and \ensuremath{\mu} denote order (spin) and disorder variables, respectively. We also derive the explicit form of the magnetization profile at the bulk critical temperature in an Ising strip of infinite length and finite width, with spin-up boundary conditions on one edge and spin-down boundary conditions on the other.

R. Z. Bariev

Per Fröjdh

The order-parameter correlation functions of the Z 2 -invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi-infinite plane constrained to fixed or free boundary conditions. These yield the corresponding universal surface exponents which distinguish the behaviour between even- and odd-critical models. We also make explicit the interplay between duality and boundary conditions.