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The Critical Exponent $θ'$ in Spin Glasses

Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent $θ'$ is obtained. From the scaling relation $λ=d/z-θ'$, the dynamic exponent z is estimated.