Absorbing-state transitions and self-organized criticality

5 problems

• Avalanche size exponent of the two-dimensional Abelian sandpile

  Open

  The Bak-Tang-Wiesenfeld sandpile is the original model of self-organized criticality. Many of its properties are known exactly, yet the power law of its avalanche sizes in two dimensions has not been determined, and it may not obey simple scaling.

• Exact critical exponents of directed percolation in 1+1 dimensions

  Open

  Directed percolation is the simplest model of spreading that can die out. In one space dimension its exponents are known to six digits from series expansions, but no exact formula exists and they do not look like simple fractions.

• Why directed percolation is rarely seen in experiments

  Partially resolved

  Theory says any spreading process with a single absorbing state and short-range interactions should follow directed percolation laws, yet clean experimental observations are few. What in real systems spoils the expected behavior is not fully understood.

• Is the Manna class distinct from directed percolation

  Contested

  Sandpile-like models in which grains are conserved show absorbing transitions that some argue form their own universality class, the Manna class. Others argue the differences are slow transients, or that the class coincides with the pinning of an elastic interface in a random medium.

• Whether self-organized criticality needs hidden fine tuning

  Contested

  Sandpile models reach criticality by themselves only when grains are added infinitely slowly and lost only at the edges, which are tuned limits in disguise. Whether any natural system shows criticality without such hidden tuning is unresolved.