Javier M. Magán, Auditya Sharma
We provide a concrete and systematic connection between the statistical physics of the Ising ferromagnet on a Cayley tree, which is an old solved problem, and the study of memory in exponentially expanding spaces, which is of current interest. We provide the order parameters which clearly signal the (known) phase transitions. The correlators are found in a new simple way, which may be of interest for other tree like systems, and which allows the computation of higher order expectation values of the order parameter. Numerical Monte Carlo simulations are used to make transparent the existence of the two different transition temperatures.
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http://arxiv.org/abs/1304.7008
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