Boundary critical behaviour of two-dimensional random Potts models

Details Boundary critical behaviour of two-dimensional random Potts models Boundary critical behaviour of two-dimensional random Potts models

1999-06-04

arxiv.org/abs/cond-mat/9906067v1

Eur. Phys. J. B, 13 (2000) 357-367

Physics

Condensed Matter

Statistical Mechanics

LaTeX2e file with EPJB, 12 pages, 14 eps figures, 10 tables

Scientific paper

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $\beta_1$ and $\beta$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $\beta_1/\nu$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.

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