CHAOTIC BEHAVIOR OF RENORMALIZATION FLOW IN A COMPLEX MAGNETIC-FIELD

It is demonstrated that decimation of the one-dimensional Ising model, with periodic boundary conditions, results in a nonlinear renormaliza tion transformation for the couplings which can lead to chaotic behavi or when the couplings are complex. The recursion relation for the coup lings under decimation is equivalent to the logistic map, or more gene rally the Mandelbrot map. In particular, an imaginary external magneti c field can give chaotic trajectories in the space of couplings. The m agnitude 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 e quation and an associated critical exponent which are identical to tho se of the Lee-Yang edge singularity in one dimension.