Nikolai Prokofiev

1.  Interacting multi-component XY-models (with or without gauge fields)
are of relevance to many fields in physics which include 
superfluid-normal and superfluid-Mott insulator QPT in neutral and charged 
liquids,  superfluid-solid QPT, Higgs mechanism in particle physics, etc. The 
question is how/whether long-range interactions mediated by gauge fields change 
the criticality of phase transitions. One possibility is that screening is 
important and criticality is not affected by the presence of gauge fields.  
Another related question is what is the proper structure of the fixed-point 
action for such models, and whether its long-range part can be universally 
described by the 1/r^2 law (in D=d+1=3).