Universal fluctuations in correlated systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated equilibrium and nonequilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state. We discuss the relationship with both Gaussian and extremal statistics.

[1]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[2]  Kinzig,et al.  Self-similarity in the distribution and abundance of species , 1999, Science.

[3]  J. Pinton,et al.  Universality of rare fluctuations in turbulence and critical phenomena , 1998, Nature.

[4]  Universal magnetic fluctuations in the two-dimensional XY model , 1998 .

[5]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality , 1998 .

[6]  S. Bramwell,et al.  Magnetic fluctuations in a finite two-dimensional model , 1997 .

[7]  M. Mézard,et al.  Universality classes for extreme value statistics , 1997, cond-mat/9707047.

[8]  V. Loreto,et al.  A "Tetris-Like" Model for the Compaction of Dry Granular Media , 1997, cond-mat/9705195.

[9]  Plischke,et al.  Width distribution for (2+1)-dimensional growth and deposition processes. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Zia,et al.  Width distribution for random-walk interfaces. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Sneppen,et al.  Self-organized pinning and interface growth in a random medium. , 1992, Physical review letters.

[12]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[13]  S. Edwards,et al.  The surface statistics of a granular aggregate , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  K. Mellanby.  How Nature works , 1978, Nature.

[15]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[16]  Alan Stuart,et al.  Statistics of extremes , 1960 .