if written as a traditional Feynman diagram according to figure 1-2. Such diagrams
have been selectively summed before, but the novelty offered in this picture is that
configurations away from Q 1, t' = 0 take all other planar diagrams into account, in
an average way. In other words, the treatment of solid lines as in the mean-field approach
allows for a different way of organizing Feynman diagrams and approximating differently,
namely across all Feynman loop orders.
The Monte Carlo approach, presented in chapter 4, offers yet another approach. It
treats the solid lines mentioned above in a stochastic way. The terms selective-summation
or importance-sampling, often seen in Monte Carlo applications of statistical physics,
describe quite well how this approach works. A closer look, and a more meaningful one, is
reserved for chapter 4.