Abstract
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.
Highlights
Condensed matter is an aggregate of interacting particles
Inner electrons are tightly bound to the nucleus and form ion cores
It is instructive to explore the effects of statistical interactions produced by particular shapes in a setting where particle energies do not factor in
Summary
Condensed matter is an aggregate of interacting particles. The interactions operate in hierarchies regarding strength and range. The common strategy of many approaches is to transform specific aspects of the strongly interacting ion cores and electrons into more weakly interacting collective modes The latter share many attributes with fundamental particles including energy-momentum relations, spin, and exclusion statistics. In the search for particles that are free of interaction energies, attention had to be paid to the requirement that the implantation of a tag or hybrid into a host (or a tag into hybrid) leaves the sums of aligned and anti-aligned nnn bonds invariant. Our search for free particles that generate the entire spectrum from this state configured as pseudo-vacuum has produced M = 4 compacts with motifs and specifications compiled in table 5.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
