Figure 2. Best-fit mean-field LFT model captures the phase transition in the square lattice.

a, A sign change of the effective interaction βJ signals the transition from antiferro- to ferromagnetic states. b, The effective energy barrier, βa²/(4b) when a < 0 and zero when a > 0 (Supplementary Sec. 5), decreases with the gap size w, reflecting increased susceptibility to fluctuations. c, The spin V_min minimizing the single-spin potential (Supplementary Sec. 5) decreases with w in agreement with the decrease in the RMS vortex spin (Fig. 1k). Each point in a–c represents an average over ≥ 5 movies in 3 μm bins at 1.5 μm intervals; blue circles are from distribution fitting, red diamonds are from SDE regression, and vertical bars indicate standard errors (Methods). d-f, Examples of the effective single-spin potential ${\mathcal{V}}^{\text{eff}}$ conditional on the mean spin of adjacent vortices [V]_V. Data (points) and estimated potential (surface) for three movies with gap widths 6, 10 and 17 μm.