# Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses

## Abstract

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.

- Authors:

- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL (United Kingdom)
- Institut fuer Theoretische Physik, Universitaet Goettingen, Friedrich-Hund-Platz 1, 37077, Goettingen (Germany)
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

- Publication Date:

- OSTI Identifier:
- 20861547

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 26; Other Information: DOI: 10.1103/PhysRevLett.97.267202; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; CONFORMAL INVARIANCE; FRACTALS; GEOMETRY; MATHEMATICAL EVOLUTION; QUANTUM FIELD THEORY; SPIN GLASS STATE; STOCHASTIC PROCESSES; TRANSFORMATIONS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Amoruso, C., Moore, M. A., Hartmann, A. K., and Hastings, M. B..
```*Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVLETT.97.267202.

```
Amoruso, C., Moore, M. A., Hartmann, A. K., & Hastings, M. B..
```*Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses*. United States. doi:10.1103/PHYSREVLETT.97.267202.

```
Amoruso, C., Moore, M. A., Hartmann, A. K., and Hastings, M. B.. Sun .
"Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses". United States.
doi:10.1103/PHYSREVLETT.97.267202.
```

```
@article{osti_20861547,
```

title = {Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses},

author = {Amoruso, C. and Moore, M. A. and Hartmann, A. K. and Hastings, M. B.},

abstractNote = {We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.},

doi = {10.1103/PHYSREVLETT.97.267202},

journal = {Physical Review Letters},

number = 26,

volume = 97,

place = {United States},

year = {Sun Dec 31 00:00:00 EST 2006},

month = {Sun Dec 31 00:00:00 EST 2006}

}

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