Abrupt transition in a sandpile model.

We present a fixed energy sandpile model which, by increasing the initial energy, undergoes, at the level of individual configurations, a discontinuous transition. The model is obtained by modifying the toppling procedure in the Bak-Tang-Wiesenfeld (BTW) [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] rules: the energy transfer from a toppling site takes place only to neighboring sites with less energy (negative gradient constraint) and with a time ordering (asynchronous). The model is minimal in the sense that removing either of the two above-mentioned constraints (negative gradient or time ordering) the abrupt transition goes over to a continuous transition as in the usual BTW case. Therefore, the proposed model offers a unique possibility to explore at the microscopic level the basic mechanisms underlying discontinuous transitions.

[1]  Per Bak,et al.  How Nature Works , 1996 .

[2]  Pietronero,et al.  Renormalization scheme for self-organized criticality in sandpile models. , 1994, Physical review letters.

[3]  R. Dickman,et al.  Self-organized criticality as an absorbing-state phase transition , 1997, cond-mat/9712115.

[4]  S. Lübeck,et al.  UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS , 2004 .

[5]  H. Stanley,et al.  FIRST-ORDER TRANSITION IN THE BREAKDOWN OF DISORDERED MEDIA , 1996, cond-mat/9612095.

[6]  Short-period attractors and non-ergodic behavior in the deterministic fixed-energy sandpile model , 2002, cond-mat/0207674.

[7]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[8]  Alessandro Vespignani,et al.  How self-organized criticality works: A unified mean-field picture , 1997, cond-mat/9709192.

[9]  Ben-Hur,et al.  Universality in sandpile models. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Renormalization of one-dimensional avalanche models , 1997 .

[11]  Dynamically driven renormalization group , 1996, cond-mat/9603052.

[12]  Loreto,et al.  Renormalization of Nonequilibrium Systems with Critical Stationary States. , 1996, Physical review letters.

[13]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[14]  A Vespignani,et al.  Avalanche and spreading exponents in systems with absorbing states. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  K. Eftaxias,et al.  Monitoring of a preseismic phase from its electromagnetic precursors. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Energy Constrained Sandpile Models , 1997, cond-mat/9712127.

[17]  Didier Sornette,et al.  Mapping Self-Organized Criticality onto Criticality , 1994, adap-org/9411002.

[18]  A. Díaz-Guilera.  Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena , 1994, cond-mat/9403036.

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

[20]  A. Malakis,et al.  Universality Aspects of Self-Organization Models , 2004 .

[21]  Hwa,et al.  Avalanches, hydrodynamics, and discharge events in models of sandpiles. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  D. Sornette,et al.  Tricritical Behavior in Rupture Induced by Disorder , 1997 .

[23]  S. S. Manna.  Two-state model of self-organized criticality , 1991 .

[24]  M. A. Muñoz,et al.  Paths to self-organized criticality , 1999, cond-mat/9910454.

[25]  Alessandro Vespignani,et al.  Order parameter and scaling fields in self-organized criticality , 1996, cond-mat/9612158.

[26]  Self-Organized Criticality in Stick-Slip Models with Periodic Boundaries , 1997, cond-mat/9704153.