Studies of Vector Spin Glasses at Low Temperatures

I briefly review the theory of spin glasses, including interaction disorder (frustration) versus spin configuration disorder, emphasizing the special features of vector spin glasses. I then develop two topics; both depend on the rotational symmetry for vector spins, represented by an O(m) matrix "order parameter" R(x),(' )and on the assumption of low temperatures. First, in Chap. I, I consider a vector spin glass with weak anisotropy. I show how to go from the microscopic to the macroscopic Hamiltonian, and apply the results to the statics and electron spin resonance modes. Second, in Chap. III, I develop approaches to the description of the local minima ("ground states") of anisotropy-free vector spin glasses in terms of topological defects of R(x).(' )These defects are defined relatively from comparisons of one local minimum to another, not by comparing with an ideal ordered state. I discuss the nature and density of the degrees of freedom characterizing the differences between the local minima. I give special attention to the role of longitudinal (in the sense of "non-rotational") fluctuations of the order parameter in the free energy, defects, and correlation functions. In Chap. IV I apply the ideas of Chap. III by comparing local minima generated by computer simulations of a Heisenberg spin glass (Edwards -Anderson model on 12 x 12 x 12 lattice). I find that "disclinations" (line defects) can exist, but conjecture that "reflections" (wall defects associated with the "longitudinal" degree of freedom) would better describe the relation of two local minima. The number of spins corresponding to a degree of freedom in constructing minima is found to be 100-200 spins.