Finite Size Scaling Analysis of Exact Ground States for +J Spin Glass Models in Two Dimens.pdfVIP

Finite Size Scaling Analysis of Exact Ground States for ±J Spin Glass Models in Two Dimensions 6 9 9 1 Naoki Kawashima(∗) and Heiko Rieger(∗∗) c e D (∗) Department of Physics, Toho University, Miyama 2-2-1, Funabashi 274, Japan (∗∗) HLRZ c/o Forschungszentrum J¨ulich, 52425 J¨ulich, Germany 2 1 February 1, 2008 ] n n PACS. 75.10.Nr, 75.50.Lk, 05.50.+q — Spin Glass, Random Systems, Ising models - s i d . Abstract. — With the help of exact ground states obtained by a polynomial algorithm t a we compute the domain wall energy ∆ at zero-temperature for the bond-random and the m site-random Ising spin glass model in two dimensions. We find that in both models the - d stability of the ferromagnetic and the spin glass order ceases to exist at a unique con- n centration pc for the ferromagnetic bonds. In the vicinity of this critical point, the size o and concentration dependency of the first and second moment of the domain wall energy c [ are, for both models, described by a common finite size scaling form. Moreover, below 1 this concentration the stiffness exponent turns out to be slightly negative θS = −0.056(6) v indicating the absence of any intermediate spin glass phase at non-zero temperature. 6 1 1 2 1 Since Edwards and Anderson (EA) proposed the model for spin glasses, it has been 6 discussed not only among researchers specialized for the subject, but in a rather wide com- 9 munity of physicists working on random systems in general. Perhaps, this is largely because / t the EA model is the simplest possible model with short-ranged interaction for which we a m might expect a spin glass phase tran