TY - JOUR

T1 - The p -adic Ising model in an external field on a Cayley tree

T2 - periodic Gibbs measures

AU - Mukhamedov, F. M.

AU - Rahmatullaev, M. M.

AU - Tukhtabaev, A. M.

AU - Mamadjonov, R.

N1 - Publisher Copyright:
© 2023, Pleiades Publishing, Ltd.

PY - 2023/8

Y1 - 2023/8

N2 - Abstract: We consider the generalized Gibbs measures corresponding to the p -adic Ising model in an external field on the Cayley tree of order two. It is established that if p\equiv 1\,(\operatorname{mod}\, 4) , then there exist three translation-invariant and two G_2^{(2)} -periodic non-translation-invariant p -adic generalized Gibbs measures. It becomes clear that if p\equiv 3\,(\operatorname{mod}\, 4) , p\neq3 , then one can find only one translation-invariant p -adic generalized Gibbs measure. Moreover, the considered model also exhibits chaotic behavior if |\eta-1|_p<|\theta-1|_p and p\equiv 1\,(\operatorname{mod}\, 4) . It turns out that even without |\eta-1|_p<|\theta-1|_p , one could establish the existence of 2 -periodic renormalization-group solutions when p\equiv 1\,(\operatorname{mod}\, 4) . This allows us to show the existence of a phase transition.

AB - Abstract: We consider the generalized Gibbs measures corresponding to the p -adic Ising model in an external field on the Cayley tree of order two. It is established that if p\equiv 1\,(\operatorname{mod}\, 4) , then there exist three translation-invariant and two G_2^{(2)} -periodic non-translation-invariant p -adic generalized Gibbs measures. It becomes clear that if p\equiv 3\,(\operatorname{mod}\, 4) , p\neq3 , then one can find only one translation-invariant p -adic generalized Gibbs measure. Moreover, the considered model also exhibits chaotic behavior if |\eta-1|_p<|\theta-1|_p and p\equiv 1\,(\operatorname{mod}\, 4) . It turns out that even without |\eta-1|_p<|\theta-1|_p , one could establish the existence of 2 -periodic renormalization-group solutions when p\equiv 1\,(\operatorname{mod}\, 4) . This allows us to show the existence of a phase transition.

KW - Ising model

KW - p -adic generalized Gibbs measure

KW - p -adic numbers

KW - periodicity

KW - phase transition

KW - translation invariance

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U2 - 10.1134/S0040577923080123

DO - 10.1134/S0040577923080123

M3 - Article

AN - SCOPUS:85169136928

SN - 0040-5779

VL - 216

SP - 1238

EP - 1253

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

IS - 2

ER -