Thomas O’Roarke Elementary

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Dilute Algebras and Solvable Lattice Models

The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is discussed.Comment: 8 pages, uuencoded gz-compressed PostScript, to appear in the proceedings of the satellite meeting of STATPHYS 19, `Statistical Models, Yang-Baxter Equation and Related Topics', August 8-10, 1995, Tianjin, Chin

Duality and conformal twisted boundaries in the Ising model

There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper symmetry of the model at criticality. Thus, at criticality, the duality-twisted Ising model is translationally invariant, similar to the more familiar cases of periodic and antiperiodic boundary conditions. The complete finite-size spectrum of the Ising quantum chain with this peculiar boundary condition is obtained

Quanta transfer in space is conserved

The paper is replaced by a new version (12-2019): DOI: 10.5281/zenodo.3572846 Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the “aggregated” quantum fields