of α and β . The bulk densities obtained using the two methods differ by ≤ 1 . 6%. Thus the MC method captures the behavior found using the Langevin equation to good precision. FIG. 4: Comparison between profiles obtained using LS (open symbols) and MC (filled symbols), α = 0 . 3 (lower curves), α = 0 . 8 (upper curves), β = 0 . 4 , L = 100. We perform MC simulations of systems of L = 100, 200 and 500 wells. Far from the phase transition, density profiles depend only weakly on system size, but near the transition there are significant finite-size effects, as illustrated in Fig. 5. In this case, as L increases, the profile tends to a near-constant value except for a sharp increase near the exit. To minimize boundary effects we study the bulk density ρ , defined as the mean density over the 10% of sites nearest the center: ρ = 10 L 0 . 55 L ∑ i =0 . 46 L ρ ( i ) . (17) 12 0 20 40 60 80 100 i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (i)