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Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature

Abstract : For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong Disorder renormalization procedure at zero temperature. In each disordered sample, the difference between the ground states associated to Periodic and Anti-Periodic boundary conditions defines a system-size Domain Wall. The numerical study in dimensions $d=2$ (up to sizes $2048^2$) and $d=3$ (up to sizes $128^3$) yields fractal Domain Walls of dimensions $d_s(d=2) \simeq 1.27$ and $d_s(d=3) \simeq 2.55$ respectively.
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Cécile Monthus. Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature. Fractals, World Scientific Publishing, 2015, 23 (04), ⟨10.1142/S0218348X15500425⟩. ⟨cea-01322516⟩

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