Elementary excitations and avalanches in the Coulomb ... - PhysioNet

obust and does not require fine tuning. In fact, we observe a divergent cutoff for other valuesof of K near 1/2, when performing hopsinin orderof of increasing hopping length insteadof of uniformlyat at random, and even for huge disorder (W = 32).Avalanche distribution for dipole insertionp(S) p(S)10 10 -2 -210 10 -3 -310 10 -4 -410 10 -5 -5W =2L L = = 8816 1630 3060 60! S -3/2A(a,L) L 3/2 3/2 p(S)10 10 0010 10 -1 -110 10 -2 -210 10 -3 -3L L = 8816 1630 3060 60(2 (2") ") -1/2 xx -3/2 exp(-x/a)a = 0.4810 10 -1 -1 10 10 00 10 10 11 10 10 2210 10 11 10 10 -1 -1 10 10 00SS // LFigure cutoff 3. 3. diverging Avalanche linearly size distribution with L scale free Figure p(S) 4. ∼ Scaling S −τ extrapolating plotof of the avalanche to L = ∞for dipole-triggered avalanches.Thesize distribution assuming Eq.(5) withdata are averaged over 20000, 48000,τ = 3/2 and S c c = aL. A(a, L) is isp(S) ∼ S −τ exp(−S/S 29000, 2135 samples for L =8, 16, c ) τ ≃ 1.530, 60a normalization Consistent factor with slowly mean-fieldvaryingrespectively. S with L, exponent computed analytically τ =3/2from thec = aL a ≃ 0.5branching process model.normalization:also Although well fitted these by results p(S) may ∼ Ssuggest −τ exp[−(S/S an analogy c ) 2 ]with the self-organizedA(a, L) critical=λ(L)/(1 avalanches− e −λ(L) ) of ofthe SK model, we argue that they τ ≃ 1.7 can be understood more simplyλ(L) in in terms − 1 −of of ln λ(L) the elementary = (aL) −1