and the phase diagram for the ground states encoded in these wave functions by means of an analysis of the equivalent classical statistical system of dimers and holes for the RK Hamiltonians of Section \[sec:hamiltonians\]. In Section \[sec:mean-field\] we summarize the results of a mean-field theory for both non-interacting and interacting classical dimer models at finite doping. The details of the mean-field theory are presented in Appendix \[app:mean-field-details\], where we compute the hole-hole correlation function and derive a qualitative phase diagram as a function of hole density and dimer interaction parameters. The main result of this simple mean-field theory is that the phase diagram at finite hole density contains two phases, a dimer-hole fluid and a columnar dimer solid. The columnar-liquid transition is continuous at weak coupling and turns first order at a tricritical point. Naturally, the critical and tricritical behavior are not correctly described by the mean-field theory, although the general topology of the phase diagram is correct and, remarkably, even the location of the tricritical point is consistent with what we find in the MC simulations of Section \[sec:MC\].

In Section \[sec:exact-critical-behavior\] we present a detailed analytic theory of the critical behavior of interacting classical dimers. Sections \[sec:zero-density\] 