Monte Carlo simulation of $1+1$-dimensional $\phi^4$ quantum field   theory
  We report results of a Monte Carlo simulation of the $\phi^4$ quantum field theory using multigrid simulation techniques and a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and large couplings. 
Wolfhard Janke and Tilman Sauer