\[sec:MC\] yield a tricritical point at a location quite consistent with these values.

Another correct prediction of the mean-field theory is the behavior of the connected hole density correlation function deep in the dimer-hole liquid phase. This prediction, also discussed in detail in Appendix \[app:mean-field-details\], fits surprisingly well the Monte Carlo simulations of Krauth and Moessner,[@krauth03] performed for a system of classical non-interacting ($u=0$) dimers at finite hole density. The mean-field result is consistent with the simulations for a quite broad region of densities even quite close to the fully packed limit $z \to 0$ where, naturally, a wrong correlation length exponent is predicted.

Phase Diagram and Correlations for Interacting Dimers and Holes {#sec:exact-critical-behavior}
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We now turn to a more precise analysis of the phase transitions of the interacting classical dimer models as a function of hole density on interaction parameter $u$. Here we take advantage of a wealth of information and methods from two-dimensional systems, exact solutions and conformal field theory, to analyse the behavior in detail and extract conclusions that will be quite useful for the analysis of the wave functions. We begin with a discussion of the undoped case, and then discuss the physics at finite 