A central limit theorem for lattice gauge Gibbs random fields (Q1335398)

\textit{E. Seiler} [Gauge theories as a problem of constructive quantum field theory and statistical mechanics (Springer, 1982)] introduced the lattice gauge theories, in which the discrete gauge fields theories were described by the lattice Gibbs random fields model. For the lattice gauge theories with finite Abelian group \(G\) in the weak coupling regime, it was shown that there is only one translation invariant Gibbs state in the infinite volume [see \textit{C. Borgs}, Commun. Math. Phys. 96, 251-284 (1985)]. This paper discusses the central limit theorem for energy variables under this Gibbs state. The previous sufficient conditions of the central limit theorem for energy variables [see \textit{B. S. Nahapetian}, Random fields. Rigorous results in statistical mechanics and quantum field theory, Esztergom 1979, Colloq. Math. Soc. János Bolyai 27, 799-820 (1981; Zbl 0487.60082)] were checked with difficulty in the lattice gauge theories.