Defect concepts for vector spin glasses

Abstract

The “order parameter” for describing low-temperature configurations of an m-vector spin glass is an O( m) orthogonal matrix R( x ), representing a rotation of one configuration relative to another, which is relatively slowly varying in space. The meaning of a “defect” description of the low-lying metastable states is clarified and the topologically stable defects and textures of R( x ) are reviewed. R( x ) is generalized to a more general ( m × m matrix) order parameter with longitudinal degrees of freedom, which in a hydrodynamic picture are associated with a longitudinal spin-stiffness constant and a spin-configuration “flattening” energy. It is shown that, in the most useful form of the Edwards-Anderson correlation function, the longitudinal fluctuations must be projected out. The relation of “defect” pictures to the phenomenological “two-level system” models and to experiments is discussed. Independent measures of the volume per defect can be derived from (i) the Edwards-Anderson correlation function, and (ii) the number of local minima in large systems. It is noted that in the limit m → ∞, (defect separation) ⪢ (core size) ⪢ (nearest-neighbor distance).