Ground State Studies of Spin Glass Models.

The ground state energy and degeneracy for a set of spin glass models, PQR models, has been studied in detail. For the pure frustration case, a subset of the general PQR case, we have studied the spacial distribution of frustrated plaquettes at T = 0. We investigated the "frustration -frustration" correlation function, which involved a series expansion analysis and a computer analysis, to examine a phase transition mechanism proposed by Schuster (1981). Schuster suggested that a pair of plaquettes is bound together above, and dissociated below a critical concentration of antiferromagnetic bonds. Our analysis, however, led us to conclude that there is no sharp "unbinding" of frustration pairs. We have developed an efficient algorithm to compute the ground state energy and degeneracy of sample PQR lattices and have studied the general PQR model numerically. Our algorithm is similar in essence to Morgenstern and Binder's (1980) transfer matrix approach used to calculate the partition function of a sample of spins in the pure frustration case. The algorithm involves computing times of order ALM 2('L), where L is the width of the lattice, M is the length, and A is a constant of proportionality. We have used the results of our analysis to investigate the possibility of a paramagnetic (<--->) spin glass phase transition in the PQR model at T = 0. Although scatter in our results for the ground state degeneracy/spin obscures evidence of a possible non-analyticity in this function, we do see evidence of a "break" in the curves for the ground state energy/spin. We have used this "break" to plot the phase transition line between the spin glass and paramagnetic regimes.