The anisotropic Ashkin-Teller model: a renormalization group study

The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the square lattice. The correlation length $(\nu_T)$ and crossover $(\phi)$ critical exponents are also calculated. With the only exception of the four-state Potts critical point, the entire phase diagram belongs to the Ising universality class.Comment: 3 ps figures, accepted for publication in Physica

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction $(J_2< 0)$ and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis

Numerical study of the spin-1 Ashkin-Teller model

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