Concentration Expansion Study of the Randomly Dilute Ising Ferromagnet with Second Neighbor Interaction

The critical properties of the randomly dilute Ising ferromagnet are discussed for the square lattice by the method of concentration expansion. The studies are mostly limited to the investigation of the effects of the second neighbor interaction on the concentration dependence of the Curie temperature T c ( p ) and on the temperature dependence of the critical exponent γ(θ) describing the susceptibility divergence. The series obtained is analysed by the root, ratio, and Padé approximant methods, respectively. As for T c ( p ), the previous results are reconfirmed by raising the degree of series expansion. The present calculation gives an apparent temperature dependence of γ(θ) and its behavior can be compared with the results previously calculated for some three-dimensional lattices. Furthermore, it is found that the essential feature of γ(θ) is not affected by the presence of the second neighbor interaction.