Translation‐invariant generalized P ‐adic Gibbs measures for the Ising model on Cayley trees
نویسندگان
چکیده
منابع مشابه
On Gibbs Measures of P -adic Potts Model on the Cayley Tree
We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ∈ Qp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ∈ pN and p ≥ 3 (resp. q ∈ 2N, p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ∈ pN if p ≥ 3 and q ∈ 2N if p = 2.
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We show this configuration in Figure 1. We calculate that the energy of this configuration is HΛ(σ|σ) = 0. We can calculate the energy of this configuration in a different way, using line segments separating lattice points with different spins, as follows. For an n × n square, there are 2n(n + 1) nearest neighbor interactions. Put a line segment between every two lattice points with different s...
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ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2020
ISSN: 0170-4214,1099-1476
DOI: 10.1002/mma.7088