Ground-state magnetization in the infinite-size limit of the 2D XY spin glass with binary disorder

Establish whether the ground state of the two-dimensional XY spin glass with nearest-neighbor binary ±1 couplings has a non-zero magnetization in the limit of infinite system size L→∞.

Background

The authors review the computational complexity of determining ground states in XY spin glasses and summarize numerical studies limited to relatively small sizes. Due to these limitations, the presence or absence of macroscopic magnetization in the true ground state as L→∞ has remained unsettled.

This question connects directly to the Kuramoto order parameter in the corresponding frustrated oscillator system and is central for distinguishing ferromagnetic ordering from spin-glass behavior in two dimensions with binary couplings.