Numerical Simulations of Random Phase Sine-Gordon Model and   Renormalization Group Predictions
  Numerical Simulations of the random phase sine-Gordon model suffer from strong finite size effects preventing the non-Gaussian $\log^2 r$ component of the spatial correlator from following the universal infinite volume prediction. We show that a finite size prediction based on perturbative Renormalisation Group (RG) arguments agrees well with new high precision simulations for small coupling and close to the critical temperature. 
D. J. Lancaster and J. J. Ruiz-Lorenzo