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

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

2006-11-16

arxiv.org/abs/cond-mat/0611433v1

Physical Review B 76, 020403(R) (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevB.76.020403

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.

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