{"title":"Evidence that the de Almeida-Thouless transition disappears below six dimensions.","authors":"Bharadwaj Vedula, M A Moore, Auditya Sharma","doi":"10.1103/PhysRevE.110.054131","DOIUrl":null,"url":null,"abstract":"<p><p>One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the h-T plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance r interact with each other falls as 1/r^{2σ}. In the presence of a random vector field of variance h_{r}^{2} the phase transition is in the universality class of the Ising spin glass in a field. Tuning σ is equivalent to changing the dimension d of the short-range system, with the relation being d=2/(2σ-1) for σ<2/3. We have found by numerical simulations that h_{AT}^{2}∼(2/3-σ) implying that the AT line does not exist below six dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054131"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.054131","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the h-T plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance r interact with each other falls as 1/r^{2σ}. In the presence of a random vector field of variance h_{r}^{2} the phase transition is in the universality class of the Ising spin glass in a field. Tuning σ is equivalent to changing the dimension d of the short-range system, with the relation being d=2/(2σ-1) for σ<2/3. We have found by numerical simulations that h_{AT}^{2}∼(2/3-σ) implying that the AT line does not exist below six dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.