Extraordinary transition in the two-dimensional O(n) model

Research Report MRR97-015

Extraordinary transition in the two-dimensional O(n) model

Murray T. Batchelor and John Cardy

Abstract: The 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 \geq 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 eigen-values between different sectors of the transfer matrix.

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