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Author (up) Montalva-Medel, M.; Rica, S.; Urbina, F. doi  openurl
  Title Phase space classification of an Ising cellular automaton: The Q2R model Type
  Year 2020 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals  
  Volume 133 Issue Pages 14 pp  
  Keywords  
  Abstract An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the so-called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them -which we call of type S-I, S-II, and S-III- share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 x 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation. (C) 2020 Elsevier Ltd. All rights reserved.  
  Address [Montalva-Medel, Marco; Rica, Sergio] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Avda Diagonal Torres 2640, Santiago, Chile  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0960-0779 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000520892300040 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1130  
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