This investigation employs a hierarchical lattice and renormalization-group methodology to probe the effects of competing crystal-field interactions in a Blume-Capel Ising system. Several phase diagrams have been produced in temperature–crystal-field space as the strength of the competing crosslink crystal-field interactions is varied. Each sink has been interpreted and critical exponents have been calculated for the higher-order transitions.

• Received 25 November 2008

DOI:https://doi.org/10.1103/PhysRevE.79.041126