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Renormalisation of 2D cellular automata with an absorbing state

Renormalisation of 2D cellular automata with an absorbing state
Renormalisation of 2D cellular automata with an absorbing state
We describe a real-space renormalisation scheme for non-equilibrium probabilistic cellular automata (PCA) models, and apply it to a two-dimensional binary PCA. An exact renormalisation scheme is rare, and therefore we provide a method for computing the stationary probability distribution of states for such models with which to weight the renormalisation, effectively minimising the error in the scale transformation. While a mean-field approximation is trivial, we use the principle of maximum entropy to incorporate nearest-neighbour spin-correlations in the steady-state probability distribution. In doing so we find the fixed point of the renormalisation is modified by the steady-state approximation order.
0022-4715
211-220
Weaver, Iain S.
aacee24c-9233-4104-bec7-ad15babbc45c
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Weaver, Iain S.
aacee24c-9233-4104-bec7-ad15babbc45c
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e

Weaver, Iain S. and Prugel-Bennett, Adam (2015) Renormalisation of 2D cellular automata with an absorbing state. Journal of Statistical Physics, 159 (2), 211-220. (doi:10.1007/s10955-014-1142-4).

Record type: Article

Abstract

We describe a real-space renormalisation scheme for non-equilibrium probabilistic cellular automata (PCA) models, and apply it to a two-dimensional binary PCA. An exact renormalisation scheme is rare, and therefore we provide a method for computing the stationary probability distribution of states for such models with which to weight the renormalisation, effectively minimising the error in the scale transformation. While a mean-field approximation is trivial, we use the principle of maximum entropy to incorporate nearest-neighbour spin-correlations in the steady-state probability distribution. In doing so we find the fixed point of the renormalisation is modified by the steady-state approximation order.

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Renormalisation of 2D cellular automata with an - Accepted Manuscript
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Accepted/In Press date: 24 October 2014
e-pub ahead of print date: 21 January 2015
Published date: April 2015

Identifiers

Local EPrints ID: 412232
URI: http://eprints.soton.ac.uk/id/eprint/412232
ISSN: 0022-4715
PURE UUID: c5114f89-1441-4b6a-b426-7dd88337c40a

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Date deposited: 14 Jul 2017 16:30
Last modified: 19 Jul 2019 18:09

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