Susceptibility divergence of the spin 1 Ising model on the Cayley tree |
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| Institution: | 1. Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany;2. Bogolyubov Institute for Theoretical Physics, 14-b, Metrolohichna str., 03680 Kiev, Ukraine;3. Institute for Theoretical Physics, Johann Wolfgang Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany;1. Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany;2. International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario, Lagoa Nova, Natal, RN 59078-970, Brazil;3. Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN 59078-970, Brazil;1. Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan;2. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan |
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| Abstract: | The temperature T2(1), below which the zero-field isothermal susceptibility diverges for the spin 1 Ising model on the M-generation Cayley tree, in the limit as M → ∞, is located. The general approach follows closely that of Falk for the spin problem. Pruning and retraction identities are used to find upper and lower bounds on the bond-length dependence of the general two-spin correlation function and thence on the susceptibility. A conjecture is advanced regarding the divergence of the higher-order susceptibilities. |
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