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.
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