The -adic Ising model in an external field on a Cayley tree: periodic Gibbs measures

The -adic Ising model in an external field on a Cayley tree: periodic Gibbs measures

We consider the generalized Gibbs measures corresponding to the -adic Ising model in an external field on the Cayley tree of order two. It is established that if , then there exist three translation-invariant and two -periodic non-translation-invariant -adic generalized Gibbs measures. It becomes cl...

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Veröffentlicht in:Theoretical and mathematical physics 2023, Vol.216 (2), p.1238-1253
Hauptverfasser: Mukhamedov, F. M., Rahmatullaev, M. M., Tukhtabaev, A. M., Mamadjonov, R.
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Applications of Mathematics
Invariants
Ising model
Mathematical and Computational Physics
Phase transitions
Physics
Physics and Astronomy
Theoretical
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creator Mukhamedov, F. M.
Rahmatullaev, M. M.
Tukhtabaev, A. M.
Mamadjonov, R.
description We consider the generalized Gibbs measures corresponding to the -adic Ising model in an external field on the Cayley tree of order two. It is established that if , then there exist three translation-invariant and two -periodic non-translation-invariant -adic generalized Gibbs measures. It becomes clear that if , , then one can find only one translation-invariant -adic generalized Gibbs measure. Moreover, the considered model also exhibits chaotic behavior if and . It turns out that even without , one could establish the existence of -periodic renormalization-group solutions when . This allows us to show the existence of a phase transition.
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639/766/189
639/766/530
639/766/747
Applications of Mathematics
Invariants
Ising model
Mathematical and Computational Physics
Phase transitions
Physics
Physics and Astronomy
Theoretical
title The -adic Ising model in an external field on a Cayley tree: periodic Gibbs measures
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