The \(\mathrm{GL}(n,\mathbb F_p)\)-invariance of the Potts Hamiltonian (Q1363182)

A specific mean-field Potts model is defined on a discrete subset of the \(n\)-torus, seen both as a lattice and as the finite field \(\mathbb F_q\) with \(q=p^n\), \(p\) a prime. This model allows for an exact computation by means of multiplicative characters (it is designed for this purpose). As a consequence, the invariance of the total energy is shown under an arbitrary change of basis of \(\mathbb F_q\) seen as an \(n\)-dimensional vector space over \(\mathbb F_p\).