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.