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 (1)

• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

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• Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Numerical study on Schramm-Loewner Evolution in nonminimal conformal field theories
• Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition
• Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent
• SLE on doubly-connected domains and the winding of loop-erased random walks
• Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass
• Domain wall entropy of the bimodal two-dimensional Ising spin glass
• Stochastic Loewner Evolution