  Critical phenomena and Goldstone mode effects in spin models with O(n)
rotational symmetry are considered. Starting with the Goldstone mode
singularities in the XY and O(4) models, we briefly review different
theoretical concepts as well as state-of-the art Monte Carlo simulation
results. They support recent results of the GFD (grouping of Feynman diagrams)
theory, stating that these singularities are described by certain nontrivial
exponents, which differ from those predicted earlier by perturbative
treatments. Furthermore, we present the recent Monte Carlo simulation results
of the three-dimensional Ising model for very large lattices with linear sizes
up to L=1536. These results are obtained, using a parallel OpenMP
implementation of the Wolff single cluster algorithm. The finite-size scaling
analysis of the critical exponent eta, assuming the usually accepted
correction-to-scaling exponent omega=0.8, shows that eta is likely to be
somewhat larger than the value 0.0335 +/- 0.0025 of the perturbative
renormalization group (RG) theory. Moreover, we have found that the actual data
can be well described by different critical exponents: eta=omega=1/8 and
nu=2/3, found within the GFD theory.
