The critical behavior 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 \ensuremath{\varphi}=(\ensuremath{\alpha}/\ensuremath{\nu}) varies continuously and is positive so that the randomness is relevant, and different critical behavior 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 behavior of the disordered model is compared with the critical behavior of an anisotropic Ashkin-Teller model, which is used as a reference 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 ${\mathit{T}}_{\mathit{c}}$ , C\ensuremath{\sim}lnL for the random-bond Ashkin-Teller and four-state Potts models and C\ensuremath{\sim}ln lnL for the random-bond Ising model.The critical behavior 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 \ensuremath{\varphi}=(\ensuremath{\alpha}/\ensuremath{\nu}) varies continuously and is positive so that the randomness is relevant, and different critical behavior 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 behavior of the disordered model is compared with the critical behavior of an anisotropic Ashkin-Teller model, which is used as a reference 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 ${\mathit{T}}_{\mathit{c}}$, C\ensuremath{\sim}lnL for the random-bond Ashkin-Teller and four-state Potts models and C\ensuremath{\sim}ln lnL for the random-bond Ising model.

arXiv:cond-mat/9411046Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsApr 1, 199567 citations

Critical interfaces of the Ashkin–Teller model at the parafermionic point

Marco Picco, Raoul Santachiara

We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.

arXiv:1005.0493Journal of Statistical Mechanics Theory and ExperimentJul 30, 201011 citations

Random-Field Correlations and Quantum Critical Phenomena

Dimo I. Uzunov, E. R. Kokutcheva, YONKO T. MILLEV

De Gruyter eBooksDec 31, 19850 citations

{\mathit{T}}_{\mathit{c}}

, C\ensuremath{\sim}lnL for the random-bond Ashkin-Teller and four-state Potts models and C\ensuremath{\sim}ln lnL for the random-bond Ising model.