Fractals and chaos related to Ising-Onsager lattices. Ternary approach versus binary approach

被引：1

作者：

Lawrynowicz, Julian ^{[1
,2
]}

Suzuki, Osamu ^{[3
]}

Niemczynowicz, Agnieszka ^{[4
]}

Nowak-Kepczyk, Magorzata ^{[5
]}

机构：

[1] Univ Lodz, Fac Phys & Appl Informat, Pomorska 149-153, PL-90236 Lodz, Poland

[2] Polish Acad Sci, Inst Math, Sniadeckich 8,POB 21, PL-00956 Warsaw, Poland

[3] Nihon Univ, Coll Humanities & Sci, Dept Comp & Syst Anal, Setagaya Ku, Sakurajosui 3-25-40, Tokyo 1568550, Japan

[4] Univ Warmia & Mazury, Dept Anal & Differential Equat, Sloneczna 54, PL-10710 Olsztyn, Poland

[5] State Sch Higher Educ Chelm, Inst Math & Informat, Pocztowa 54, PL-22100 Chelm, Poland

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2018年 / 15卷 / 11期

关键词：

Ternary alloy; binary alloy; composition algebra; crystal lattice; fractals;

D O I：

10.1142/S0219887818501876

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In connection with several attempts to extend Onsager's (1944) crystal statistics to three dimensions keeping the spirit of the original ising's (1925) model, we suggest to involve binary and ternary extension of triangles in connection with fractals and chaos, following the ideas of Kikuchi (1951). We apply ternary Clifford algebras in addition to the usual (binary) Clifford algebras and identify two ternaries with three ternaries with the help of noncommutative Galois extension. In some sense, the paper continues the ideas of Lawrynowicz, Marchiafava and Nowak-Kgpczyk (2006), and Kerner and Suzuki (2012) published in this journal.

引用

页数：17

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