Abrupt transition in a sandpile model

Abstract

We present a fixed energy sandpile (FES) 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 BTW rules: the energy transfer from a toppling site takes place only to neighbouring 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 an unique possibility to explore at the microscopic level the basic mechanisms underlying discontinuous transitions.

7 pages, 5 figures

References in corpus (15)

• Universal scaling behavior of non-equilibrium phase transitions
• Paths to Self-Organized Criticality
• First-Order Transition in the Breakdown of Disordered Media
• How self-organized criticality works: A unified mean-field picture
• Tri-critical behavior in rupture induced by disorder
• Self-organized criticality as an absorbing-state phase transition
• Avalanche and spreading exponents in systems with absorbing states
• Universality in Sandpile Models
• Order Parameter and Scaling Fields in Self-Organized Criticality
• Mapping Self-Organized Criticality onto Criticality
• Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena
• Energy constrained sandpile models
• Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model
• Dynamically Driven Renormalization Group
• Self-organized criticality in stick-slip models with periodic boundaries