Minimal Unitary Models and The Closed SU(2)-q Invariant Spin Chain

We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We project a particular class of statistical models belonging to the unitary minimal series. A particular model corresponds to a particular value of the coupling constant. The operator content is derived. This class of models has charge-dependent boundary conditions. In simple cases (Ising, 3-state Potts) corresponding Hamiltonians are constructed. These are non-local as the original spin chain.Comment: 19 pages, latex, no figure

Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction

Local height probabilities in a composite Andrews-Baxter-Forrester model

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.Comment: 34 pages, 5 figures; v2: expanded introduction, references added and other minor change

Exceptional structure of the dilute A3_3 model: E8_8 and E7_7 Rogers--Ramanujan identities

The dilute A$_3$ lattice model in regime 2 is in the universality class of the Ising model in a magnetic field. Here we establish directly the existence of an E$_8$ structure in the dilute A$_3$ model in this regime by expressing the 1-dimensional configuration sums in terms of fermionic sums which explicitly involve the E$_8$ root system. In the thermodynamic limit, these polynomial identities yield a proof of the E$_8$ Rogers--Ramanujan identity recently conjectured by Kedem {\em et al}. The polynomial identities also apply to regime 3, which is obtained by transforming the modular parameter by $q\to 1/q$. In this case we find an A_1\times\mbox{E}_7 structure and prove a Rogers--Ramanujan identity of A_1\times\mbox{E}_7 type. Finally, in the critical $q\to 1$ limit, we give some intriguing expressions for the number of $L$-step paths on the A$_3$ Dynkin diagram with tadpoles in terms of the E$_8$ Cartan matrix. All our findings confirm the E$_8$ and E$_7$ structure of the dilute A$_3$ model found recently by means of the thermodynamic Bethe Ansatz.Comment: 9 pages, 1 postscript figur

Response of Foraminifera to Anthropogenic Nicotine Pollution of Cigarette Butts: An Experimental Approach

The most often dispersed environmental pollutants that are released both directly and indirectly into the environment that may eventually reach aquatic ecosystems and contaminate aquatic biomes are cigarette butts (CBs). Toxicants such as nicotine, dangerous metals, total particulate matter, and recognized carcinogens can be introduced and transported via CBs into aquatic ecosystems. The examination of the effects of synthetic nicotine on three different species of cultured benthic foraminifera was the focus of this study. Three foraminiferal species from three distinct biomineralization pathways were specifically examined for viability and cellular ultrastructure, including the calcareous perforate Rosalina globularis, the calcareous imperforate Quinqueloculina spp., and the agglutinated Textularia agglutinans. The survival rate, cellular stress, and decalcification were used to assess the toxicological effects of synthetic nicotine. We were able to analyze the reaction of major macromolecules and calcium carbonate to this pollutant using FTIR (Fourier Transform Infrared) spectroscopy. High Performance Liquid Chromatography (HPLC) study was performed to increase our understanding of nicotine bioavailability in the medium culture. Different acute experiments were performed at different dates, and all indicated that synthetic nicotine is acutely hazardous to all three cultured foraminiferal taxa at lethal and sublethal concentrations. Each species responded differently depending on the type of shell biomineralization. Synthetic nicotine enhances shell decalcification and affects the composition of cytoplasmic macromolecules such as lipids and proteins, according to the FTIR spectroscopy investigations. The lipid content rose at lethal concentrations, possibly due to the creation of vesicles. The proteins signal evidences general cellular dyshomeostasis. The integration among the acute toxicity assay, synchrotron, and chemical HPLC analyses provided a valuable approach for the assessment of nicotine as a biomarker of exposure to the toxicants associated with smoking and the impact of this emerging and hazardous material on calcifying marine species