  The concept of jamming has attracted great research interest due to its broad
relevance in soft matter such as liquids, glasses, colloids, foams, and
granular materials, and its deep connection to the sphere packing problem and
optimization problems. Here we show that the domain of amorphous jammed states
of frictionless spheres can be significantly extended, from the well-known
jamming-point at a fixed density, to a jamming-plane that spans the density and
shear strain axes. We explore the jamming-plane, via athermal and thermal
simulations of compression and shear jamming, with a help of an efficient swap
algorithm to prepare initial equilibrium configurations. The jamming-plane can
be divided into reversible-jamming and irreversible-jamming regimes, based on
the reversibility of the route from the initial configuration to jamming. Our
results suggest that the irreversible-jamming behavior reflects an escape from
the meta-stable glass basin to which the initial configuration belongs to, or
the absence of such basins. All jammed states, either compression or shear
jammed, are isostatic, and exhibit jamming criticality of the same universality
class. However, the anisotropy of contact networks non-trivially depends on the
jamming density and strain. Among all state points on the jamming-plane, the
jamming-point is a unique one with the minimum jamming density and the maximum
randomness. For lattice packings, the jamming-plane shrinks into a single shear
jamming-line that is independent of initial configurations. Our study paves the
way for solving the long-standing random close packing problem, and provides a
more complete framework to understand jamming.
