Physics – Mathematical Physics
Scientific paper
2005-10-06
Lett. Math. Phys. 70(2004), 17--28
Physics
Mathematical Physics
12 pages
Scientific paper
We consider a nearest-neighbor $p$-adic $\l$-model with spin values $\pm 1$ on a Cayley tree of order $k\geq 1$. We prove for the model there is no phase transition and as well as the unique $p$-adic Gibbs measure is bounded if and only if $p\geq 3$. If $p=2$ then we find a condition which guarantees nonexistence of a phase transition. Besides, the results are applied to the $p$-adic Ising model and we show that for the model there is a unique $p$-adic Gibbs measure.
Khamraev Murod
Mukhamedov Farrukh
Rozikov Utkir
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