Self-organized criticality

Ole Peters and Nicholas Moloney have worked on self-organized criticality (SOC). While many different ideas of what SOC actually is are present in the literature, we approached this from the perspective of non-equilibrium statistical mechanics, where SOC is a sub-branch of critical phenomena. Here, the idea is that there’s a continuous phase transition whose critical point is somehow attractive to the dynamics of the system. So the system approaches this point and stays close to it, displaying scale-freedom and diverging correlation lengths, very much like an equilibrium system at criticality. The precise mechanism of self-organization is not known.

Nicholas has written a book about SOC with Kim Christensen: Complexity and Criticality

O. Peters and G. Pruessner
Tuning- and order parameter in the SOC ensemble.
arXiv:0912.2305v1 (2009).

O. Peters and M. Girvan,
Universality under conditions of self-tuning.
J. Stat. Phys. 141, 1, 53–59 (2010).
arXiv:0902.1956v2
doi:10.1007/s10955-010-0039-0

G. Pruessner and O. Peters,
Reply to “Comment on ‘Self-Organized Criticality and Absorbing States: Lessons from the Ising Model'”.
Phys. Rev. E 77, 048102 (2008).
doi: 10.1103/PhysRevE.77.048102

G. Pruessner and O. Peters,
Self-Organized Criticality and Absorbing States: Lessons from the Ising Model.
Phys. Rev. E 73, 025106(R) (2006).
doi: 10.1103/PhysRevE.73.025106

K. Christensen, N. Moloney, O. Peters and G. Pruessner,
Avalanche Behavior in an Absorbing-State Oslo Model.
Phys. Rev. E. 70, 067101(R) (2004).
doi: 10.1103/PhysRevE.70.067101