  Motivated by puzzling spin-glass behaviors observed in many pyrochlore-based
magnets, effects of magnetoelastic coupling to local lattice distortions were
recently studied by the authors for a bond-disordered antiferromagnet on a
pyrochlore lattice [Phys. Rev. Lett. 107, 047204 (2011)]. Here, we extend the
analyses with focusing on the critical property of the spin-glass transition
which occurs concomitantly with a nematic transition. Finite-size scaling
analyses are performed up to a larger system size with 8192 spins to estimate
the transition temperature and critical exponents. The exponents are compared
with those in the absence of the magnetoelastic coupling and with those for the
canonical spin-glass systems. We also discuss the temperature dependence of the
specific heat in comparison with that in canonical spin-glass systems as well
as an experimental result.
