Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field

Dolan, Brian P. (1994) Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field. (Preprint)

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Abstract

It is demonstrated that decimation of the one dimensional Ising model, with periodic boundary conditions, results in a non-linear renormalisation transformation for the couplings which can lead to chaotic behaviour when the couplings are complex. The recursion relation for the couplings under decimation is equivalent to the logistic map, or more generally the Mandelbrot map. In particular an imaginary external magnetic field gives chaotic trajectories in the space of couplings, not for all values of the field but for a set of values which is dense in the real numbers. The magnitude of the field must be greater than a minimum value which tends to zero as the critical point T = 0 is approached.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:11
Last Modified: 18 Jul 2018 14:20
URI: http://dair.dias.ie/id/eprint/710

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