We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with +/- J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E_0, by an amount quadratic in E_0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition disappears.
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