  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.
