The random bond Ising model on the Bethe lattice

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Abstract
The paper studies the random bond Ising model of a spin glass of a tree of coordination number q=3. The model is studied as an example of the method of ring recurrence. A set of recursion relations between the moments of the probability distribution of the order parameter are produced. It is shown that solutions of the recursion relations exist which form an infinite bifurcating set below a critical temperature tau c. The nature of the first such solution is investigated in detail and the critical exponent analogous to beta is found.

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