Ising-Type and Other Transitions in One-Dimensional Coupled Map Lattices with Sign Symmetry |
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| Authors: | C Boldrighini L A Bunimovich G Cosimi S Frigio A Pellegrinotti |
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| Institution: | (1) Dipartimento di Matematica G. Castelnuovo, Università  La Sapienza, , Piazzale Aldo Moro 5, 00185 Roma, Italy;(2) Southeast Applied Analysis Center; School of Mathematics, Georgia Insitute of Technology, Atlanta, Georgia, 30332;(3) Dipartimento di Matematica e Fisica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy;(4) Dipartimento di Matematica, Universitá degli studi di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy |
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| Abstract: | We consider a one-dimensional lattice of expanding antisymmetric maps –1, 1] –1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter  is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as grows beyond some critical value c. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system. |
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| Keywords: | chaotic systems coupled map lattices phase transitions Ising-type transitions |
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