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[[File:Cayley Tree Branch with Branching Ratio = 2.jpg|thumb|An Open Cayley Tree or Branch with Branching Ratio = 2 and k Generations]]
In order to investigate an Ising model with potential relevance for large (e.g. with <math>10^4</math> or <math>10^5</math> interactions per node) neural nets, at the suggestion of Krizan in 1979, {{harvtxt|Barth|1981}} obtained the exact analytical expression for the free energy of the Ising model on the closed [[Cayley tree]] (with an arbitrarily large branching ratio) for a zero-external magnetic field (in the thermodynamic limit) by applying the methodologies of {{harvtxt|Glasser|1970}} and {{harvtxt|Jellito|1979}}
<math display="block">-\beta f = \ln 2 + \frac{2\gamma}{(\gamma+1)} \ln (\cosh J) + \frac{\gamma(\gamma-1)}{(\gamma+1)} \sum_{i=2}^z\frac{1}{\gamma^i}\ln J_i (\tau) </math>
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