and \[sec:finite-density\] focus on the field-theoretic Coulomb-gas approach for this model at zero and finite doping, respectively. We show that, up to a critical value of a parameter, the undoped RK wave function describes a critical system with continuously varying critical exponents, with a phase transition (belonging to the 2D KT universality class) to a state with long-range columnar order. At finite hole doping we find a hole-dimer liquid phase (with short-range correlations) and a stable phase with long-range columnar order. At low hole densities the phase boundary is a line of fixed points with varying exponents ending at a KT-type multicritical point where the transition becomes first order. We present a field-theoretical treatment of this tricritical point and a theory of the evolution of the behavior of the columnar and orientational order parameters and of their susceptibilities along the phase boundary. Past the tricritical point the system is found to exhibit a strong tendency to phase separation, which we verify in our numerical simulations (Section \[sec:MC\]). In Section \[sec:hole-int\] we consider the effects of direct hole-hole interactions near the first-order phase boundary, and discuss one of the many inhomogeneous phases which arise in this regime instead of phase separation.

