Nonuniversal exponents in sandpiles with stochastic particle number transfer

TL;DR

This paper investigates fixed density sandpile models with stochastic particle transfer, deriving the critical density analytically and demonstrating that critical exponents vary continuously with the transfer probability parameter.

Contribution

It provides an exact calculation of the critical density and shows that critical exponents are nonuniversal and depend on the stochastic transfer parameter p.

Findings

Critical density is exactly determined.

Critical exponents vary continuously with p.

Static and dynamic critical exponents are nonuniversal.

Abstract

We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing transition occurs is found exactly. We study the critical behavior numerically and find that the exponents associated with both static and time-dependent quantities vary continuously with $p$.