  The statistical mechanics of particles with shapes on a one-dimensional
lattice is investigated in the context of the $s=1$ Ising chain with uniform
nearest-neighbor coupling, quadratic single-site potential, and magnetic field,
which supports four distinct ground states:
$|\uparrow\downarrow\uparrow\downarrow...>$, $|\circ\circ...>$,
$|\uparrow\uparrow...>$, $|\uparrow\circ\uparrow\circ...>$. The complete
spectrum is generated from each ground state by particles from a different set
of six or seven species. Particles and elements of pseudo-vacuum are
characterized by motifs (patterns of several consecutive site variables).
Particles are floating objects that can be placed into open slots on the
lattice. Open slots are recognized as permissible links between motifs. The
energy of a particle varies between species but is independent of where it is
placed. Placement of one particle changes the open-slot configuration for
particles of all species. This statistical interaction is encoded in a
generalized Pauli principle, from which the multiplicity of states for a given
particle combination is determined and used for the exact statistical
mechanical analysis. Particles from all species belong to one of four
categories: compacts, hosts, tags, or hybrids. Compacts and hosts find open
slots in segments of pseudo-vacuum. Tags find open slots inside hosts. Hybrids
are tags with hosting capability. In the taxonomy of particles proposed here,
`species' is indicative of structure and `category' indicative of function. The
hosting function splits the Pauli principle into exclusion and accommodation
parts. Near phase boundaries, the state of the Ising chain at low temperature
is akin to that of miscible or immiscible liquids with particles from one
species acting as surfactant molecules.
