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The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighborcoupling is used to construct a system of floating particles characterized bymotifs of up to six consecutive local spins. The spin couplings cause theassembly of particles which, in turn, remain free of interaction energies evenat high density. All microstates are configurations of particles from one ofthree different sets, excited from pseudo-vacua associated with ground statesof periodicities one, two, and four. The motifs of particles and elements ofpseudo-vacuum interlink in two shared site variables. The statisticalinteraction between particles is encoded in a generalized Pauli principle,describing how the placement of one particle modifies the options for placingfurther particles. In the statistical mechanical analysis arbitrary energiescan be assigned to all particle species. The entropy is a function of theparticle populations. The statistical interaction specifications aretransparently built into that expression. The energies and structures of theparticles alone govern the ordering at low temperature. Under specialcircumstances the particles can be replaced by more fundamental particles withshorter motifs that interlink in only one shared site variable. Structuresemerge from interactions on two levels: particles with shapes from coupledspins and long-range ordering tendencies from statistically interactingparticles with shapes.

Interlinking motifs and entropy landscapes of statistically interacting particles