Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass
| dc.creator | Fisch, Ronald | |
| dc.date | 2007-03-06 | |
| dc.date | 2007-10-01 | |
| dc.date.accessioned | 2026-07-07T08:51:01Z | |
| dc.date.available | 2026-07-07T08:51:01Z | |
| dc.description | The ground state entropy of the 2D Ising spin glass with +1 and -1 bonds is studied for $L \times M$ square lattices with $L \le M$ and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. From this we obtain the domain wall entropy as a function of $L$ and $M$. It is found that for domain walls which run in the short, $L$ direction, there are finite-size scaling functions which depend on the ratio $M / L^{d_S}$, where $d_S = 1.22 \pm 0.01$. When $M$ is larger than $L$, very different scaling forms are found for odd $L$ and even $L$. For the zero-energy domain walls, which occur when $L$ is even, the probability distribution of domain wall entropy becomes highly singular, and apparently multifractal, as $M / L^{d_S}$ becomes large. | |
| dc.description | 13 pages, 7 figures; final version, to appear in J. Stat. Phys | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0703137 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0703137 | |
| dc.identifier | J. Stat. Phys. 130, 561 (2008) | |
| dc.identifier | doi:10.1007/s10955-007-9436-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144795 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Statistical Mechanics | |
| dc.title | Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass | |
| dc.type | text |