Talk:Critical Phenomena: field theoretical approach
I do not understand how the Markovian property of the mapping may fail and therefore why it is an assumption.
I believe that one should also say something about the real space renormalization group and may be about the hierarchical model where the renormalization group is exact.
Answer to question 1: not every transformation in the space of Hamiltonians is Markovian and even less Markovian stationary. I guess the question is motivated by the class of transformations the referee has in mind when thinking about the renormalization group. But in fact the class of transformations could be larger than was is usually considered. However, what the assumptions emphasize is that only transformations that share these properties lead to useful conclusions.
2-Indeed, other topics like real space renormalization group or hierarchical models could also have been discussed, but these topics are not directly in the spirit of the article and to keep the length of the article reasonably short, choices had to be made. But there is always the possibility to add a reference and I am open to suggestions.