ムカイダ　ヒサミツ   MUKAIDA Hisamitsu   向田　寿光    所属   埼玉医科大学  医学部 教養教育    職種   教授
論文種別	学術雑誌(原著)
言語種別	英語
査読の有無	査読あり
表題	Griffiths-Type Theorems for Short-Range Spin Glass Models
掲載誌名	正式名：Journal of Statistical Physics 略　 称：J. Stat. Phys ISSNコード：15729613
掲載区分	国外
出版社	Springer Science and Business Media LLC
巻・号・頁	191(28)
総ページ数	30
著者・共著者	◎Chigak Itoi, Hisamitsu Mukaida, Hal Tasaki
発行年月	2024/02/23
概要	We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap R1,2 implies the non-differentiability of the two-replica free energy with respect to the replica coupling parameter λ. In Z2 invariant models such as the standard Edwards–Anderson model, the non-differentiability is equivalent to the spin glass order characterized by a nonzero Edwards–Anderson order parameter. This general- ization of Griffiths’ theorem is proved for any short-range spin glass models with classical bounded spins. We also prove that the non-differentiability of the two-replica free energy mentioned above implies replica symmetry breaking in the literal sense, i.e., a spontaneous breakdown of the permutation symmetry in the model with three replicas. This is a general result that applies to a large class of random spin models