Summary: Physica A 257 (1998) 303306
Replica mean ˙eld theory for granular media
Jeferson J. Arenzon
Instituto de FĂsica, UFRGS CP 1505191501-970, Porto Alegre RS, Brazil
An in˙nite range spin-glass-like model for granular systems is introduced and studied through
the replica mean ˙eld formalism. Equilibrium properties under vibration and gravity are ob-
tained, as well as the phase diagram showing the dependence on gravity, density and vibration.
c 1998 Elsevier Science B.V. All rights reserved.
Besides industrial applications, the unusual static and ow properties of granular
materials [1,2] o er a challenging problem from the theoretical point of view, and
despite the enormous e ort that has been devoted in recent years, they are far from
being fully understood. At a ˙xed macroscopic density, a granular system may be in
a large number of di erent microscopic states, that has lead to the introduction of a
statistical mechanics description of powders [3,4], replacing the energy by the volume
and the temperature by the compactivity. On the other hand, in analogy with the
thermal motion in liquids and gases, a granular temperature has also been introduced,
which depends on the motions of the particles, in contrast with the compactivity that
characterizes a static system.
These systems, composed of many discrete macroscopic particles, present slow re-