  This paper reports numerical studies of a compressible version of the Ising
spin glass in two dimensions. Compressibility is introduced by adding a term
that couples the spin-spin interactions and local lattice deformations to the
standard Edwards-Anderson model. The relative strength of this coupling is
controlled by a single dimensionless parameter, mu. The timescale associated
with the dynamics of the system grows exponentially as mu is increased, and the
energy of the compressible system is shifted downward by an amount proportional
to mu times the square of the uncoupled energy. This result leads to the
formulation of a simplified model that depends solely on spin variables;
analysis and numerical simulations of the simplified model predict a critical
value of the coupling strength above which the spin-glass transition cannot
exist at any temperature.
