Group structure optimalization for cell-spin transformations in multi-dimensional interaction spaces

A criterion of minimal deviation from exact semi-group properties is applied to a second-order cumulant expansion of a linear renormalization transformation for the two-dimensional Ising model with three interactions.Mechanisms that influence the validity of group structure and the selectivity of the criterion, such as the way in which the Hamiltonian is divided into a free part H₀ and a perturbation V, are examined in detail.For the critical exponent y_H, related to the optimal value for the free parameter of the transformation, a great improvement is found over previous calculations with only one interaction.