Lukic J, Galluccio A, Marinari E, Martin O C, Rinaldi G
Dipartimento di Fisica, SMC and UdR1 of INFM, INFN, Università di Roma La Sapienza, Piazzale le Aldo Moro 2, 00185 Roma, Italy.
Phys Rev Lett. 2004 Mar 19;92(11):117202. doi: 10.1103/PhysRevLett.92.117202. Epub 2004 Mar 18.
We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low lying excitations and by the way low energy domain walls proliferate in this model.
我们计算了具有二元耦合的二维伊辛自旋玻璃的精确配分函数。在这些系统中，基态具有高度简并性，并且与第一激发态之间存在大小为4J的能隙。然而，我们发现低温比热密度按exp(-2J/T)缩放，对应于大小为2J的“有效”能隙；此外，一个相关的交叉长度尺度按exp(J/T)增长。我们通过低能激发的简并性以及低能畴壁在该模型中的增殖方式来证明这些缩放关系。
