Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

Abstract

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts-Bethe mapping over for the prime numbers. In fact, for ✓ OK Manage Cookies ❯ 8/14/2018 Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Im plies the Vastness of the Set of p-Adic Gibbs M…

$P$-adic monomial equations and their perturbation

“…We notice that the obtained result allows to investigate dynamical behavior of the function f b,c,d , for certain particular values of the parameters, chaoticity of such type of function has been investigated in [2,18].…”

Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

“…However, the Potts model has a much richer phase structure, which makes it an important testing ground for new theories and algorithms in the study of critical phenomena. The scope of research for the q-state Potts Model extend to its critical manifolds (Scullard & Jacobsen, 2016), its topological phases in the antiferromagnetic configuration (Zhao et al, 2018), its static critical behavior in high resolution (Caparica et al, 2015), fraction of uninfected walkers in its one-dimensional model (O'Donoghue & Bray, 2002), its ferromagnetic states with multisite interaction (Schreiber et al, 2018), its disordered states without a ferromagnetic phase (Marinari et al (1999), Carlucci (1999), approximate theories of first-order phase transitions on its twodimensional model (Dasgupta & Pandit, 1987) [which has Critical exponents of domain walls (Dubail et al, 2010), critical polynomials Jacobsen & Scullard (2013), entanglement entropy measurable using wavelet analysis Tomita (2018)], periodic p-adic Gibbs Measures Ahmad et al (2018), local scale invariance in ageing (Lorenz & Janke, 2007), Potts glass models (Yamaguchi, 2015), percolation models on bowtie lattices (Ding et al, 2012), Roughness exponent in two-dimensional percolation, and clock model (Redinz & Martins, 2001), interfacial adsorption in two-dimensional pure and random-bond Potts models (Fytas et al, 2017), exact valence bond entanglement entropy and probability distribution in the XXX Spin Chain (Jacobsen & Saleur, 2008), lung cancer pathological image analysis using a hidden Potts model (Li et al, 2017), the cellular Potts model (He et al (2009), Durand & Guesnet (2016), Albert & Schwarz (2014), Albert & Schwarz (2014), Voss-Böhme (2012), R. Noppe et al (2015), Scianna & Preziosi (2014), Harrison & Vasiev (2008)), the two (2)-Dimensional Wetting transition (Lopes & Mombach, 2017), the random resistor network and its...…”

The study on general cubic equations over p-adic fields

“…In fact, all results in this paper are extension and unification of the previous results. Meanwhile, applications of quadratic and cubic equations in the p-adic lattice models of statistical mechanics were presented in the papers [1,2,23,25,29,30,33]. We would like to stress that quadratic and cubic equations have naturally arisen in the investigations of p-adic Gibbs measures of Potts models on Cayley trees.…”