Spin glasses for the infinitely long ranged bond Ising model and for the short ranged binary bond Ising model without use of the replica method

✍ Scribed by Shigetoshi Katsura; Sakari Inawashiro; Sumiyoshi Fujiki

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 632 KB
• Volume: 99
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(79)90130-4

✦ Synopsis

The long ranged Gaussian random Ising bond model and short ranged binary random Ising bond model are discussed by the method of the pair approximation of the cluster variation and by the method of the integral equation for the distribution function of the effective fields. For the long ranged model, Sherrington and Kirkpatrick's result is generalized and rederived without use of the replica method. For the short ranged model, i.e. a binary mixture of JA = -JB, the integral equation is solved exactly and the energy of the spin glass state is obtained at T = 0.