Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

Abstract

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE${}_{\kappa }$. Multiple tests are consistent with SLE${}_{\kappa }$, where $\kappa =2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.

4 pages, 3 figures, see related work by Amoruso, Hartmann, Hastings, Moore at cond-mat/0601711

References in corpus (13)

• SLE for theoretical physicists
• 2D growth processes: SLE and Loewner chains
• Conformal invariance in two-dimensional turbulence
• Critical Behavior of Random Bond Potts Models
• Conformal Algebras of 2D Disordered Systems
• Triviality of the Ground State Structure in Ising Spin Glasses
• Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses
• Minimum spanning trees on random networks
• Winding angle variance of Fortuin-Kasteleyn contours
• Dipolar SLEs
• Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• On the Red-Green-Blue Model

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