  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.
