Cohen Tervaert, Gerard (2019) About ising and potts models on cayley trees and bayesian networks. Master's Thesis / Essay, Mathematics.
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Abstract
We perform numerical estimates for the q-state Potts model on a k-order Cayley tree. Külske, Rozikov and Khakimov explicitly calculated up to 2^q − 1 TISGMs (Translation Invariant Splitting Gibbs Measures) for the binary tree (k = 2), without an external field (α = 0). We extend these results numerically for k > 2 and α ≠ 0. We conjecture that for α ≥ k − 1 the model has niqueness. Additionally, decay of memory is proved for a Potts-type model on a Bayesian network with up to two parents and a counterexample is given for a more general case.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Enter, A.C.D. van |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 12 Mar 2019 |
| Last Modified: | 13 Mar 2019 08:46 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/19261 |
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