Chaos in p-adic Statistical Lattice Models: Potts Model

p$$ p $$‐Adic phase transitions for countable state Potts model

“…We point out that statistical interpretations of these $$$ p $$$‐adic probabilities have been discussed in previous studies [15, 20]. The development of a $$$ p $$$‐adic version of the Kolmogorov's theorem [21, 22] offered further investigation of statistical mechanics models in the context of $$$ p $$$‐adic probability theory [23]. A main question of the lattice models in the $$$ p $$$‐adic statistical mechanics is to describe $$$ p $$$‐adic Gibbs measures and detect phase transitions.…”

“…The offered approach opens new insight in better understanding hidden properties of the physical models. First, $$$ p $$$‐adic lattice models have been appeared in the literature [24–28] to investigate phase transition issues of certain $$$ p $$$‐adic models over Cayley trees (see Mukhamedov and Khakimov [23] for recent review). In previous works [29–36], using chaotic behavior of the $$$ p $$$‐adic renormalization group (dynamical systems approach) technique, it has been established vastness of the set of $$$ p $$$‐adic Gibbs measures for the Potts models on a Cayley tree.…”