Continuous phase transition, finite-size scaling

FIG. 14 Phase diagram of the quantum APR model in the Q -T plane. The solid curve shows the line of continuous phase transitions from an ordered phase at low temperatures and small rotational constants to a disordered phase according to the mean-field approximation. The symbols show the transitions found by the finite-size scaling analysis of the path integral Monte Carlo data. The dashed line connecting these data is for visual help only. (Reprinted with permission from Ref. 328, Fig. 2. 1997, American Physical Society.)... 

Using the finite-size scaling method, study of the analytical behavior of the energy near the critical point shows that the open-shell system, such as the lithium-like atoms, is completely different from that of a closed-shell system, such as the helium-like atoms. The transition in the closed-shell systems from a bound state to a continuum resemble a first-order phase transition, while for the open-shell system the transition of the valence electron to the continuum is a continuous phase transition [9]. 

Quantum dimers provide models for anti-ferromagnets. Using a combination of continuous-time lattice diffusion Monte Carlo [56] and RQMC, the square lattice quantum dimer model for lattice sizes up to 48 x 48 sites was investigated to estimate the location of the columnar to plaquette phase transition [57], The former phase has no parallel dimers, while the latter one has sets of plaquettes with parallel dimers continuously changing orientation. The author found significant finite-size corrections to scaling for the plaquette phase and liquid phase. 

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