We analyse the zero-temperature behaviour of the XY Edwards–Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a specially tailored evolutionary method, resulting in the genetic embedded matching (GEM) approach, allows for the computation of numerically exact ground states for relatively large systems. This enables a thorough reinvestigation of the long-standing questions of (i) extensive degeneracy of the ground state and (ii) a possible decoupling of spin and chiral degrees of freedom in such systems. The new algorithm together with appropriate choices for the considered sets of boundary conditions and finite-size scaling techniques allows for a consistent determination of the spin and chiral stiffness scaling exponents.
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Weigel, M., & Gingras, M. J. P. (2007). Spin and chiral stiffness of the XY spin glass in two dimensions. Journal of Physics: Condensed Matter, 19(14), . https://doi.org/10.1088/0953-8984/19/14/145217