{"title":"Frustration in the Ising model on a decorated square lattice.","authors":"F A Kassan-Ogly, A V Zarubin","doi":"10.1103/PhysRevE.111.044133","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we performed the comprehensive studies of magnetic frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers-Wannier transfer matrix method. The assigned challenge consisted in finding rigorous formulas for residual entropies of all possible cases of degeneration of the system without exception and also elucidating the influence of frustrations on the behavior of the thermodynamic functions of the system under discussion. The accomplished results turned out to be very rich and intricate, especially in comparison with the original undecorated square lattice, in which frustration properties are completely absent. Such an abundance of properties is due to the multiparametric problem of decorated lattice with four exchange interactions J_{x}, J_{y}, J_{dx}, and J_{dy} taking on arbitrary continuous values and different signs: positive (ferromagnetic) and negative (antiferromagnetic), as well as with two discrete variables d_{x} and d_{y} (multiplicities of decorating spins in both lattice directions), corresponding to infinite natural series of numbers.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"111 4-1","pages":"044133"},"PeriodicalIF":2.4000,"publicationDate":"2025-04-01","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.111.044133","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
In this paper, we performed the comprehensive studies of magnetic frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers-Wannier transfer matrix method. The assigned challenge consisted in finding rigorous formulas for residual entropies of all possible cases of degeneration of the system without exception and also elucidating the influence of frustrations on the behavior of the thermodynamic functions of the system under discussion. The accomplished results turned out to be very rich and intricate, especially in comparison with the original undecorated square lattice, in which frustration properties are completely absent. Such an abundance of properties is due to the multiparametric problem of decorated lattice with four exchange interactions J_{x}, J_{y}, J_{dx}, and J_{dy} taking on arbitrary continuous values and different signs: positive (ferromagnetic) and negative (antiferromagnetic), as well as with two discrete variables d_{x} and d_{y} (multiplicities of decorating spins in both lattice directions), corresponding to infinite natural series of numbers.
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.