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We study the behaviour of the Binder cumulant on finite square lattices atthe Kosterlitz-Thouless phase transition. We determine the fixed point value ofthe Binder cumulant and the coefficient of the leading logarithmic correction.These calculations are supplemented with Monte Carlo simulations of theclassical XY (plane rotator) model, the Villain model and the dual of theabsolute value solid-on-solid model. Using the single cluster algorithm, wesimulate lattices up to L=4096. For the lattice sizes reached, subleadingcorrections are needed to fit the data for the Binder cumulant. We demonstratethat the combined analysis of the Binder cumulant and the second momentcorrelation length over the lattice size allows for an accurate determinationof the Kosterlitz-Thouless transition temperature on relatively small lattices.We test the new method at the example of the 2-component phi^4 model on thelattice.

The Binder Cumulant at the Kosterlitz-Thouless Transition