POWER-LAW FALLOFF IN THE KOSTERLITZ-THOULESS PHASE OF A 2-DIMENSIONAL LATTICE COULOMB GAS

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperature gb and a constant Θ>0 such that for all β>β and all external charges ξ∈R we have {Mathematical expression}, where Gξ(x) is the two-point external charges correlation function, η=dist(ξ, Z), and {Mathematical expression} for {Mathematical expression}. In the case of a hard-core or standard Coulomb gas with activity z, we may choose β=β(z) such that β(z)→24π as z↘0. © 1990 Plenum Publishing Corporation.