A new real space renormalisation method and its Julia set

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Abstract
The authors introduce a new real space renormalisation method which is valid not only on the real axis but also everywhere in the complex plane of temperatures. The method requires the knowledge of the partition function on small lattices and can in principle be improved systematically. They test this method on the two-dimensional Ising model. They find that it gives a satisfactory picture for the set of zeros of the partition function. When restricted to the real axis, the estimates for the renormalisation transformation, the critical point and the thermal exponent are also very good.

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