Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

Abstract

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.

11 pages, 16 figures, revtex

References in corpus (8)

• The two-dimensional random-bond Ising model, free fermions and the network model
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• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
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• Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses
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Cited by in corpus (12)

• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Fractal dimension of domain walls in two-dimensional Ising spin glasses
• From local to global ground states in Ising spin glasses
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts
• Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder
• Low-energy excitations in the three-dimensional random-field Ising model
• Excitations in high-dimensional random-field Ising magnets
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Nature of spin glass order in physical dimensions