DEGENERATE AND NONDEGENERATE GROUND-STATES IN BIMODAL VECTOR SPIN-GLASSES

The scaling behavior of the width of the distribution of couplings (sigma) in vector spin glasses with a bimodal bond distribution is investigated using the real-space Migdal-Kadanoff renormalization-group method. Two-dimensional systems show an exponential decay of sigma with length scale and a degenerate ground state if the rescaling parameter b is even. However, three-dimensional systems show a power-law decay of sigma for any b. These results suggest that three-dimensional bimodal vector spin glasses are much less sensitive to exact ground-state degeneracies than two-dimensional systems and, unlike the latter, may have a conventionally ordered nondegenerate ground state.