Frustration in the Ising model on a decorated square lattice.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
F A Kassan-Ogly, A V Zarubin
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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.

在装饰方形格子上的伊辛模型受挫。
在本文中,我们在基于Kramers-Wannier传递矩阵法的精确解析方法的框架下,对装饰方形晶格上的Ising模型中的磁受挫特性进行了全面的研究。指定的挑战包括找到所有可能情况下系统无一例外退化的剩余熵的严格公式,并阐明挫折对所讨论系统的热力学函数行为的影响。完成的结果变得非常丰富和复杂,特别是与原始的未经装饰的方形晶格相比,其中完全没有挫折特性。如此丰富的性质是由于装饰晶格的多参数问题,具有四个交换相互作用J_{x}, J_{y}, J_{dx}和J_{dy}取任意连续值和不同符号:正(铁磁)和负(反铁磁),以及两个离散变量d_{x}和d_{y}(装饰自旋在两个晶格方向上的多重性),对应于无限自然数列。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
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.
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