Existence of p-Adic Quasi Gibbs Measures for Mixed Type p-Adic Ising λ-Model

We consider nearest-neighbors and next nearest-neighbors p-adic Ising λ-model with spin values {∓ 1} on a Cayley tree of order two. First we prove that the model satisfies the Kolmogorov consistency condition and then we prove that the nonlinear equation corresponding to the model has at least two solutions in $Q_{p}$, where p is a prime number p ≥ 3. One of the roots is in $ε_{p}$ and the others are in $Q_{p}$\$ε_{p}$. If the nonlinear equation has more than one non-trivial solutions for the model then we conclude that p-adic quasi Gibbs measure exists for the model.