Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study

The critical behaviour of a bond-disordered Ashkin-Teller model on a square lattice is investigated by intensive Monte-Carlo simulations. A duality transformation is used to locate a critical plane of the disordered model. This critical plane corresponds to the line of critical points of the pure model, along which critical exponents vary continuously. Along this line the scaling exponent corresponding to randomness $\phi=(\alpha/\nu)$ varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model. We use a cluster algorithm for the Monte Carlo simulations based on the Wolff embedding idea, and perform a finite size scaling study of several critical models, extrapolating between the critical bond-disordered Ising and bond-disordered four state Potts models. The critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic Ashkin-Teller model which is used as a refference pure model. We find no essential change in the order parameters' critical exponents with respect to those of the pure model. The divergence of the specific heat $C$ is changed dramatically. Our results favor a logarithmic type divergence at $T_{c}$, $C\sim \log L$ for the random bond Ashkin-Teller and four state Potts models and $C\sim \log \log L$ for the random bond Ising model.