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On the extremality of the disordered state for the Ising model on the Bethe lattice

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Abstract

We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k≥2 is extremal if and only if β is less or equal to the spin glass transition value, given by tanh(β SGc = 1/√k.

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References

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The work was partially supported by the NSF grant DMS 9504513.

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Ioffe, D. On the extremality of the disordered state for the Ising model on the Bethe lattice. Letters in Mathematical Physics 37, 137–143 (1996). https://doi.org/10.1007/BF00416016

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  • DOI: https://doi.org/10.1007/BF00416016

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