The six-vertex F model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite-order phase transition of the Kosterlitz–Thouless type. As one of the few non-trivial exactly solved models, it provides a welcome gauge for new numerical simulation methods and scaling techniques. In view of the notorious problems of clearly resolving the Kosterlitz–Thouless scenario in the two-dimensional XY model numerically, the F model in particular constitutes an instructive reference case for the simulational description of this type of phase transition. We present a loop-cluster update Monte Carlo study of the square-lattice F model, with a focus on the properties not exactly known, such as the polarizability or the scaling dimension in the critical phase. For the analysis of the simulation data, finite-size scaling is explicitly derived from the exact solution and plausible assumptions. Guided by the available exact results, the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour.