Emergent Dynamical Ising Transition in Diffusive Sandpiles

TL;DR

This paper reveals how diffusion alters avalanche behavior in sandpile models, uncovering an emergent Ising transition linked to criticality and correlations, bridging SOC and equilibrium physics.

Contribution

It introduces a duality between diffusive sandpiles and Ising models, showing how diffusion induces a magnetic transition and changes MSS correlations.

Findings

Diffusion suppresses rare avalanches and promotes spanning avalanches.

An emergent magnetic instability coincides with a percolation transition.

MSS correlations switch from anti- to positive due to diffusion.

Abstract

Minimally stable site (MSS) clusters play a dominant role in shaping avalanches in the self-organized critical (SOC) systems. The manipulation of MSS clusters through local smoothings (diffusion) alter the MSS landscape, suppressing rare avalanches and postponing them until they manifest as spanning avalanches. By leveraging the Inverse Ising problem, we uncover a duality between diffusive sandpiles and equilibrium statistical physics. Our analysis reveals an emergent magnetic instability in the dual Ising model, coinciding with the formation of spanning avalanches and marking a transition to a correlated percolation regime. At this point, the MSS loop soups exhibit fractal self-similarity and power-law distributions, while the effective pairwise interactions in the dual system vanish, signaling a magnetic transition characterized by abrupt changes in magnetization and spin susceptibility. Crucially, we show that diffusion fundamentally reshapes avalanche dynamics: the spatial anti-correlations of MSSs in standard SOC systems transform into positive correlations when diffusion is introduced. These findings bridge self-organized criticality, percolation theory, and equilibrium phase transitions, shedding new light on emergent criticality and large-scale correlations in non-equilibrium systems.