Batchelor, Murray T.Cardy, John2026-01-012026-01-010550-3213ORCID:/0000-0001-6742-0518/work/162950034https://hdl.handle.net/1885/733799994The extraordinary transition which occurs in the two-dimensional O(n) model for n < 1 at sufficiently enhanced surface couplings is studied by conformal perturbation theory about infinite coupling and by finite-size scaling of the spectrum of the transfer matrix of a simple lattice model. Unlike the case of n ≥ 1 in higher dimensions, the surface critical behaviour differs from that occurring when fixed boundary conditions are imposed. In fact, all the surface scaling dimensions are equal to those already found for the ordinary transition, with, however, an interesting reshuffling of the corresponding eigenvalues between different sectors of the transfer matrix.The authors thank A. Owczarek for useful comments. This work was begun while J.C. was a visitor at ANU under the Mathematical Sciences Research Visitors Program. It was continued while M.B. was a visitor at Oxford under the Australian Academy of Science/Royal Society Exchange Scheme, and completed while J.C. was a visitor at the Institute for Theoretical Physics, Santa Barbara. The work of M.B. has also been supported by the Australian Research Council, and of J.C. by the EPSRC through Grant GR/J78327, and the NSF through Grant PHY94-07194.12en1997-12-0110.1016/S0550-3213(97)00533-60031498055