Cubic equations associated with p-adic potts models - Saburov, Mansoor (2015)
The p-adic models of statistical mechanics require the investigation of roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to some given domains. In this paper, we are aiming to study the solvability of general cubic equations over the set Z_p^{*} wherep>3. Our investigations enable to describe all translation invariant p-adic Gibbs measures on a Cayley tree of order three.