0 0.1 0.2 0.3 0.4 0.5 0 0.5 1 1.5 T * c NVT-MC GC-TMMC MC-TI S-SCOZA M-SCOZA  TPT MSA-EOS Eq. (5) 0 0.05 0.1 0.1 0.2 0.3 0.4 0.5 T * c FIG. 2: Relation betw een critical temperature and effective range δ (see text) of the HCAY model for different simulation and theoretical results. Symbols have the same meaning as in Fig. 1. MC- TI with 3 . 9 ≤ κ ≤ 100 from Ref. [7]. The red line represents the prediction of Eq. (5). The inset is an enlargement of the short-range region. 0 0.2 0.4 0.6 0.8 1 * 0.27 0.29 0.31 0.33 0.35 0.37 T * =12 =15 =10 =9 FIG. 3: Vapor-liquid coexistence curves of SR-HCAY fluid. Open symbols are NVT-MC data from this work. Other symbols are GC-TMMC data from Ref. [36]. Dotted lines are S-SCOZA results from this work. Starbursts and circles are S-SCOZA and M-SCOZA critical points, respectively. at low temperature, where other simulation techniques such as GEMC or GC-TMMC run into considerable difficulties, because the high liquid density of the systems makes particle insertion very time-consuming. Our simulation results for the coexistence curve are reported in Table II. Figure 3 also shows the coexistence curves and the critical points predicted 13