  The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor
coupling is used to construct a system of floating particles characterized by
motifs of up to six consecutive local spins. The spin couplings cause the
assembly of particles which, in turn, remain free of interaction energies even
at high density. All microstates are configurations of particles from one of
three different sets, excited from pseudo-vacua associated with ground states
of periodicities one, two, and four. The motifs of particles and elements of
pseudo-vacuum interlink in two shared site variables. The statistical
interaction between particles is encoded in a generalized Pauli principle,
describing how the placement of one particle modifies the options for placing
further particles. In the statistical mechanical analysis arbitrary energies
can be assigned to all particle species. The entropy is a function of the
particle populations. The statistical interaction specifications are
transparently built into that expression. The energies and structures of the
particles alone govern the ordering at low temperature. Under special
circumstances the particles can be replaced by more fundamental particles with
shorter motifs that interlink in only one shared site variable. Structures
emerge from interactions on two levels: particles with shapes from coupled
spins and long-range ordering tendencies from statistically interacting
particles with shapes.
