Dolan, Brian P. (1995) Chaotic behavior of renormalization flow in a complex magnetic field. Physical Review E, 52 (4). pp. 4512-4515. ISSN 1063-651X

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Abstract

It is demonstrated that decimation of the one-dimensional Ising model, with periodic boundary conditions, results in a nonlinear renormalization transformation for the couplings which can lead to chaotic behavior 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 can give chaotic trajectories in the space of couplings. The magnitude of the field must be greater than a minimum value which tends to zero as the critical point T=0 is approached, leading to a gap equation and an associated critical exponent which are identical to those of the Lee-Yang edge singularity in one dimension.

Item Type:	Article
Keywords:	Chaotic behavior; renormalization flow; complex magnetic field;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10504
Identification Number:	https://doi.org/10.1103/PhysRevE.52.4512
Depositing User:	Dr. Brian Dolan
Date Deposited:	19 Feb 2019 15:04
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
Refereed:	Yes
URI:	https://journals.aps.org/pre/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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