25 0 1 2 3 4 1 2 3 4 0 5 10 15 C v T 0 20 40 60 80 T 2 local global T 2 χ$^{T}$ 2 local global T 2 4 6 8 12 16 L (a) (b) (c) 4 6 8 12 16 L 4 6 8 12 16 L 4 6 8 12 16 L (d) (e) 4 6 8 12 16 L (f) 4 6 8 12 16 L 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Q 0 100 200 300 400 0.2 0.3 0.4 0.5 0.6 0.7 0.8 T FIG. 23: (Color online) Temperature dependence of (a) nematic or- der parameter [Eq. (18)], (b) heat capacity [Eq. (31)], (b) and (c) the related measure of local correlation λ local E and its susceptibility [Eqs. (10) and (11)], and (d) and (e) the global order parameter λ global E and its susceptibility [Eqs. (8) and (9)] for b = 0 . 6 , h = 0 and a range of values of system size. The results are for J$_{3}$ = − 0 . 02 , showing both a first order transition into the nematic phase at T Q = 0 . 518(6) (indicated by the vertical dotted line) and a transition into the ordered phase at T N = 0 . 42(2) (dashed line).