Table 1.

The critical exponents and their expressions

Exponent	Expression	Relations	2d measured/prediction	3d measured/prediction
θ	P(x) ∼ xθ		0.57	0.35
z	T ∼ lz		0.57	0.65
df	$S_c\sim L^{d_f}$		1.10	1.50
β	$\dot{\mathrm{\gamma }}\sim {\left(\Sigma -{\Sigma }_c\right)}^{\mathrm{\beta }}$	β = 1 + z/(d − df)	1.52/1.62	1.38/1.41
τ	ρ(S) ∼ S−τ	$\mathrm{\tau }=2-\frac{\mathrm{\theta }}{\mathrm{\theta }+1}\frac{d}{d_f}$	1.36/1.34	1.45/1.48
ν	ξ ∼ (|Σ − Σc|)−ν	ν = 1/(d − df)	1.16/1.11	0.72/0.67

The third column contains the three scaling relations we derive in the text. We compare values measured in our elasto-plastic model, both in 2d and 3d, with the predictions from the scaling relations.