Analytical approach for piecewise linear coupled map lattices

被引：12
|
作者：
Just, W [1 ]
机构：
[1] Max Planck Inst Phys Complex Syst, D-01187 Dresden, Germany
来源：
JOURNAL OF STATISTICAL PHYSICS | 1998年 / 90卷 / 3-4期
关键词：
phase transition; simplicial mapping; mean-field Ising model; symbolic dynamics;
D O I：
10.1023/A:1023272819435
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A simple construction is presented which generalizes piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. In particular, the spin Hamiltonian which is generated by the symbolic dynamics is accessible. As an example, a formal relation between a globally coupled system and an Ising mean-field model is established. The phase transition in the limit of infinite system size is analyzed and analytical results are compared with numerical simulations.
引用
收藏
页码：727 / 748
页数：22
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