Seminarium Fizyki Materii Skondensowanej

Here we are interested in the critical properties of two-dimensionalIsing model and $N$-'color' Ashkin-Teller model in a presence of randomquenched structural defects correlated with the distance $r$ according toa power-law $r^{-a}$. In our study we use a mapping of the mentioned spinmodels onto two-dimensional theory of complex (Dirac) fermionic fieldswith disorder. To study the critical behaviour we apply therenormalization group approach. Using two-loop approximation for Isingmodel we find that it belongs to new universality class characterized bythe correlation length exponent $\nu=2/a$. Applying bosonization, we alsocalculate the averaged square of the spin-spin correlation function andfind an estimate for the critical exponent $\eta$. Within one-loop orderwe find for $N$-'color' Ashkin-Teller model that a ``weakly universal''scaling behavior for $N = 2$ as well as the first-order phase transitionfor $N > 2$, are transformed by the correlated disorder into acontinuous phase transition sharing universality class with previouslyconsidered model.