The Binder cumulant at the Kosterlitz–Thouless transition

Abstract

We study the behaviour of the Binder cumulant on finite square lattices at theKosterlitz–Thouless phase transition. We determine the fixed-point value of theBinder cumulant and the coefficient of the leading logarithmic correction. Thesecalculations are supplemented with Monte Carlo simulations of the classicalXY (plane rotator) model, the Villain model and the dual of the absolute valuesolid-on-solid model. Using the single-cluster algorithm, we simulate lattices up toL = 4096. For the lattice sizes reached, subleading corrections are needed to fit the data for theBinder cumulant. We demonstrate that the combined analysis of the Binder cumulant andthe second moment correlation length over the lattice size allows for an accuratedetermination of the Kosterlitz–Thouless transition temperature on relativelysmall lattices. We test the new method on the example of the two-componentϕ4 model on the lattice.