The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions

Abstract

The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space filling. Here, the fractal dimension of domain-wall interfaces is studied using the strong-disorder renormalization group method pioneered by Monthus [Fractals 23, 1550042 (2015)] both for the Edwards-Anderson spin-glass model in up to 8 space dimensions, as well as for the one-dimensional long-ranged Ising spin-glass with power-law interactions. Analyzing the fractal dimension of domain walls, we find that replica symmetry is broken in high-enough space dimensions. Because our results for high-dimensional hypercubic lattices are limited by their small size, we have also studied the behavior of the one-dimensional long-range Ising spin-glass with power-law interactions. For the regime where the power of the decay of the spin-spin interactions with their separation distance corresponds to 6 and higher effective space dimensions, we find again the broken replica symmetry result of space filling excitations. This is not the case for smaller effective space dimensions. These results show that the dimensionality of the spin glass determines which theoretical description is appropriate. Our results will also be of relevance to the Gardner transition of structural glasses.

6 pages, 4 figures, 1 table

References in corpus (10)

• Fractal free energy landscapes in structural glasses
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?
• The correspondence between long-range and short-range spin glasses
• Fractal dimension of domain walls in two-dimensional Ising spin glasses
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Some considerations of finite dimensional spin glasses
• Fractal dimension of domain walls in the Edwards-Anderson spin glass model

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• Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions
• Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions
• Possible instability of one-step replica symmetry breaking in p-spin Ising models outside mean-field theory
• Criticality and conformality in the random dimer model
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Dynamic fractals in spatial evolutionary games
• Precursors of the Spin Glass Transition in Three Dimensions
• Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses
• Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass