FIG. 2.

(color online). Main plot: Plot of log₁₀ probability vs log₁₀ rank of the most frequent 10³ states for a system of N = 200 nonidentical, conditionally independent spins [model (a)]. Plots are an average over 200 realizations of the quenched variables h_i that break the symmetry between spins, with 5 × 10⁵ samples taken for each realization. Parameters: h_i ~ 𝒩(μ = 1, s = 0.3) and β ~ 𝒩(μ = 0, s = 2). The red line represents the least-squares fit to patterns 100–1000, slope of −1.012. Inset: Same as above, except for a model of N = 200 spins with quenched random interactions J_ij and biases h_i [model (b)]. An average over ten realizations of J_ij and h_i is chosen from J_ij ~ 𝒩(μ = 1, s = 0.5), h_i ~ 𝒩(μ = 1, s = 0.85), and β ~ 𝒩(μ = 0.5, s = 0.5), with 3 × 10⁵ samples taken for each realization. The red line represents the least-squares fit to patterns 100–1000, slope of −1.011.