首页 | 本学科首页   官方微博 | 高级检索  
     


Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model
Authors:L. A. Pastur  M. V. Shcherbina
Affiliation:(1) Mathematical Division of the Institute for Low Temperature Physics and Engineering of the Academy of Sciences of the Ukrainian SSR, 310164 47 Kharkov, USSR
Abstract:
We prove that ifHcircNis the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity
$$bar q_N  = N^{ - 1} sum leftlangle {S_l } rightrangle _H^2 $$
converges in the variance to a nonrandom limit asNrarrinfin, then the mean free energy of the model converges to the expression obtained by SK. Since this expression is known not to be correct in the low-temperature region, our result implies the ldquonon-self-averagingrdquo of the order parameter of the SK model. This fact is an important ingredient of the Parisi theory, which is widely believed to be exact. We also prove that the variance of the free energy of the SK model converges to zero asNrarrinfin, i.e., the free energy has the self-averaging property.See the Remarks after the proof of Theorem 1 on the validity of our results for more general distributions ofJij.
Keywords:Spin glasses  order parameter  self-averaging
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号