Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field

Details Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field

1994-12-06

arxiv.org/abs/cond-mat/9412031v3

Phys. Rev. E52 (1995) 4512-4515, Erratum-ibid.E53 (1996) 6590

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 figures, PlainTeX, corrected some typos

Scientific paper

10.1103/PhysRevE.52.4512

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 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 associated critical exponent which are identical to those of the Lee-Yang edge singularity in one dimension.

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