Abstract
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.
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Just, W. Analytical Approach for Piecewise Linear Coupled Map Lattices. Journal of Statistical Physics 90, 727–748 (1998). https://doi.org/10.1023/A:1023272819435
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DOI: https://doi.org/10.1023/A:1023272819435