Spin stiffness and lower critical dimension of vector spin glasses

Considerable advances have been made in recent years in the understanding of Ising spin glass models in two and three dimensions. Models with continuous degrees-of-freedom, which are often more realistic in describing physical systems, have received much less attention. We study properties of domain-wall excitations in continuous-spin glass systems by means of extensive numerical ground-state computations. Using a hybrid genetic algorithm utilizing an embedded matching approach for the case of two-dimensional, planar lattices and a combination of local spin-quench and over-relaxation moves for three-dimensional systems, we study XY and Heisenberg systems in two and three dimensions. Owned to the novel technique and the consequently larger accessible system sizes as well as elaborate finite-size scaling techniques, the corresponding spin-stiffness exponent θs is for the first time determined consistently from different sets of boundary conditions. Considering the stiffness of the system towards chiral excitations, a result different from the spin stiffness is found, strongly indicating the presence of spin-chirality decoupling for the case of the two-dimensional XY spin glass. In the limit of an infinite number of spin dimensions, the energy landscape simplifies significantly, such that considerably larger system sizes can be considered. This simplification comes about through the fact that in the limit of a large number of spin components the ground state of a finite system occupies only a finitedimensional subspace in spin space. As a consequence, for each system size there exists a finite, critical number of spin components above which the ground-state energy does not change upon further adding spin dimensions, such that the system effectively describes a spherical spin glass. Here, this observation is exploited for investigating the stability of the