Fractal dimension of domain walls in the Edwards-Anderson spin glass model

Abstract

We study directly the length of the domain walls (DW) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and Gaussian bond distributions, we have isolated the DW and have calculated directly its fractal dimension $d_f$. Our results show that, even though in three dimensions $d_f$ is the same for both distributions of bonds, this is clearly not the case for two-dimensional (2D) systems. In addition, contrary to what happens in the case of the 2D Edwards-Anderson spin glass with Gaussian distribution of bonds, we find no evidence that the DW for the bimodal distribution of bonds can be described as a Schramm-Loewner evolution processes.

arXiv comment6 pages, 5 figures. Accepted for publication in PRB

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• Domain walls and Schramm-Loewner evolution in the random-field Ising model
• Domain walls and chaos in the disordered SOS model
• The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions
• Is negative-weight percolation compatible with SLE?
• Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature
• Ground-state energy and entropy of the two-dimensional Edwards-Anderson spin-glass model with different bond distributions
• Loop erased random walk on a percolation cluster is compatible with Schramm-Loewner evolution
• q-deformed Loewner evolution