Spin stiffness of vector spin glasses

Abstract

We study domain-wall excitations for O ( m ) vector spin glasses in the limit m → ∞ , where the energy landscape is simplified considerably compared to XY or Heisenberg models due to the complete disappearance of metastability. Using numerical ground-state calculations and appropriate pairs of complementary boundary conditions, domain-wall defects are inserted into the systems and their excitation energies are measured. This allows us to determine the stiffness exponents for lattices of a range of spatial dimensions d = 2 , … , 7 . Compiling these results, we can finally determine the lower critical dimension of the model. The outcome is compared to estimates resulting from field-theoretic calculations.