Renormalization-group study of the corssover to classical behavior for an Ising model with vacancies

By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to d=4 to study the crossover to classical behavior. Up to a crossover dimension d¿3.4, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At d¿3.4, both fixed points merge, representing in this way the crossover to classical behavior. At d>3.4, indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.