Subextensive singularity in the 2D $\pm J$ Ising spin glass
| dc.creator | Fisch, Ronald | |
| dc.date | 2006-07-24 | |
| dc.date | 2007-05-15 | |
| dc.date.accessioned | 2026-07-07T08:31:53Z | |
| dc.date.available | 2026-07-07T08:31:53Z | |
| dc.description | The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d ν= 2 - α$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented. | |
| dc.description | 13 pages, 7 figures; final version, to appear in J. Stat. Phys | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0607622 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0607622 | |
| dc.identifier | J. Stat. Phys. 128, 1113 (2007) | |
| dc.identifier | doi:10.1007/s10955-007-9336-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138632 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Statistical Mechanics | |
| dc.title | Subextensive singularity in the 2D $\pm J$ Ising spin glass | |
| dc.type | text |