The effects of Repulsive Biquadratic Interactions in a Blume-Emery-Griffiths Spin-Glass with Competing, Attractive Biquadratic Cross-link Interactions

A BEG Hamiltonian is used to model an Ising spin glass with annealed vacancies on a hierarchical lattice. In addition to competing bilinear interactions, repulsive biquadratic interactions on the perimeter of our unit structures compete with attractive cross-link interactions. Ordering and transitions in this system are probed by generating several phase diagrams, using renormalization group methods, for a range of constant K/J. A physical interpretation is offered for each sink corresponding to a bulk phase in phase space and critical exponents are calculated for the higher-order transitions.