Order parameter and segregated phases in a sandpile model with two particle sizes

We study the behavior of two one-dimensional sandpile models with two different particle sizes in dependence on the size dispersion and on the difference in the surface creep between the two types of particles. We investigate the phase space and find several types of particle segregation that occur: two oppositely totally segregated states, a striped state, and two oppositely partially segregated states. By defining an order parameter for the size segregation we investigate the effect of the size dispersion and of the creep difference between the two types of particles. At very small size dispersions the creep difference induces the size segregation; if the sign of the creep difference is reversed, the size segregation in the sandpile is reversed too and the order parameter changes its sign. In one of our models, in the absence of the creep difference the order parameter: grows continuously with the size dispersion from zero to its maximal value, a behavior that is reminiscent of the behavior of the order parameter in the vicinity of a continuous phase transition in the absence of external fields.