Numerical Study of Spin and Chiral Order in a Two-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">XY</mml:mi></mml:math>Spin Glass

Abstract

The two-dimensional $\mathrm{XY}$ spin glass is studied numerically by a finite size defect energy scaling method at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite $T$. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent ${\ensuremath{\nu}}_{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\nu}}_{c}\ensuremath{\approx}2.70$. Preliminary results in 3D are also obtained.