Renormalisation group study of XY and Heisenberg models in two dimensions

Abstract

We perform a numerical study of the XY and Heisenberg models with the finite size real space renormalisation group method. We confirm the Berezinskii-Kosterlitz-Thouless picture for the XY model and provide strong evidence against a standard algebraic divergence of the correlation length. We also obtain the most accurate determination of the magnetic exponent. For the Heisenberg model, we find that the scaling law predicted by the asymptotic freedom property of the theory around zero bare coupling is fulfilled, indicating the absence of phase transitions at a non-zero temperature.