Fig. 4: Effective Ising model and Monte Carlo simulation of a Coulomb liquid droplet.
From: Evidence of Coulomb liquid phase in few-electron droplets
a, Interpretation of partitioning in terms of magnetic spin interactions. Uncorrelated partitioning (U = 0, binomial distribution in the middle), bunching (U < 0) and antibunching (U > 0) correspond, respectively, to paramagnetic, ferromagnetic and antiferromagnetic phases of the Ising model on a complete graph, for which counting statistics gives the distribution of the total magnetization. b, Phase diagram of the antiferromagnetic crossover in the thermodynamic limit of the Ising model, with appropriately scaled negative pair correlations κ2N as the order parameter. The axes are given by the temperature T and the magnetic field μ, scaled by the Néel temperature TN. The measured correlations for N = 3, 4 and 5 at μ = 0 are shown by colours in small squares. The horizontal position T/TN of the squares is obtained from the fits of the Ising model to the partitioning curves (Extended Data Table 1). The slight deviations in colour between the phase diagram and the measured values (36%, 20% and 11%, respectively) are dominated by the finite-N effect, not by discrepancy with the model. c, Four configurations of the 2D confining potential in the central channel (level lines), together with snapshots of the spatial positions of N = 5 electrons (red dots) from Monte Carlo simulations of a classical Coulomb plasma (see Methods). The colour scale shows the calculated average electron density. The four panels correspond to (from left to right) Δ − Δ0 = 101, 60, 21 and 0 mV.
