The duality transformation for the IRF models

A systematic method of performing the duality transformation for the IRF models is proposed. This is an extension of the Stephen-Mittag method to the general case. It is found that the duality transformation is closely related to the star-triangle relation.     

Quantum group symmetry of partition functions of IRF models and its application to Jones' index theory

For each Boltzmann weight of a face model, we associate two quantum groups (face algebras) which describe the dependence of the partition function on boundary value condition. Using these, we give a proof of (non-)flatness of A-D-E connections of A. Ocneanu, which is a crucial algebraic part of the classification of subfactors with Jones' index less than 4.     

The Braid Group Representation of IRF Model

The braid group representations (BGRs) corresponding to IRF model are discussed by solving the spectral-independent Yang-Baxter Equation in the cases q = 2 and 3. The BGRB obtained here are constant matrices.     

An exactly solvable 5-state IRF model

A 5-state IRF model (σ_l = 0, 1, 2, 3, 4) with a hard-core condition 0 ⩽ σ_i + σ_j ⩽ 4 on adjacent spins σ_i and σ_j is exactly solved. Explicit parametrizations of 70 independent Boltzmann weights which satisfy 510 star-triangle equations are presented with an exact expression for the free energy.     

The Evolving Etiology of Bilateral Vocal Fold Immobility

In the past, bilateral vocal fold immobility (BVFI) occurred most commonly after thyroidectomy. However, no large series documenting the etiology of adult BVFI has been published within the past fifteen years. This study reviews the etiologic patterns of BVFI at our institutions. We compare BVFI from before and after 1980. We also review combined studies of unilateral vocal fold immobility (UVFI) to compare and unilateral versus bilateral etiologic trends. In comparison with previously published series, fewer cases of BVFI present today as a complication of thyroid surgery and more as the result of malignancies and nonsurgical trauma. Unfortunately, BVFI caused by malignancy is not usually an initial sign of local disease, but an ominous sign of recurrence or metastases. In comparing UVFI and BVFI we found that thyroidectomy causes a higher percentage of BVFI than of UVFI. Over one-third of UVFI cases were caused by neoplasm which further underscores the potential seriousness of immobile vocal folds and the need for careful investigation.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

Spin models as microfoundation of macroscopic market models

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thus bear the chance for better models for market regulation. However microscopic models and macroscopic models are commonly studied separately. Here, we exemplify a unified view of a microscopic and a macroscopic market model in a case study, deducing a macroscopic Langevin equation from a microscopic spin market model closely related to the Ising model. The interplay of the microscopic and the macroscopic view allows for a better understanding and adjustment of the microscopic model, as well, and may guide the construction of agent based market models as basis of macroscopic models.     

Polymer models and generalized Potts-Kasteleyn models

The well-established relation between Potts models withv spin values and random-cluster models (with intracluster bonding favored over intercluster bonding by a factorv) is explored, but with the random-cluster model replaced by a much generalized polymer model, implying a corresponding generalization of the Potts model. The analysis is carried out in terms a given defined functionR(), an entropy/free-energy density for the polymer model in the casev=1, expressed as a function of the density of units. The aim of the analysis is to determine the analogR _v () ofR() for general nonnegativev in terms ofR(), and thence to determine the critical value of density _vg at which gelation occurs. This critical value is independent ofv up to a valuev _P, the Potts-critical value. What is principally required ofR() is that it should show a certain given concave/convex behavior, although differentiability and another regularizing condition are required for complete conclusions. Under these conditions the unique evaluation ofR _v () in terms ofR() is given in a form known to hold for integralv but not previously extended. The analysis is carried out in terms of the Legendre transforms of these functions, in terms of which the phenomena of criticality (gelation) and Potts criticality appear very transparently andv _P is easily determined. The value ofv _P is 2 under mild conditions onR. Special interest attaches to the functionR ₀(), which is shown to be the greatest concave minorant ofR(). The naturalness of the approach is demonstrated by explicit treatment of the first-shell model.     

Higgs models

This lecture presented at the Baikal summer school on physics of elementary particles and astrophysics in 2011 is devoted to the Higgs mechanism of the electroweak symmetry breaking within the Standard Model and in some models beyond it.     

Superstring-inspired models

We discuss the structure of low-energy groups arising from compactified models based on the heterotic string. Particular regard is paid to the possibility of intermediate scale breaking which may change the low-energy gauge structure and may naturally lead to doublet-triplet splitting and the suppression of proton decay. We present an illustrative example of such a model with a low energy gauge group structure SU₃^c × SU₂^L × SU₂^R × U₁^B−L which may be compatible with low-energy phenomena including limits on neutrino masses and sin²θ_W. Mechanisms leading to the minimal SU₃^c × SU₂^L × U₁^Y low-energy gauge group are also presented.     

Cosmological models

An LRS Bianchi type II cosmological model is built with a state equation that is a function of the cosmic timet. The ratiop/ is 1/3 whent 0 and is insignificant whent. Thus, the matter content behaves like radiation for smallt and like dust for larget.     

Dual-resonance models

Dual-resonance models are treated both as S-matrix theories and as systems of interacting strings. We show how Veneziano was able to construct a dual four-point amplitude with narrow resonances and rising Regge trajectories. The construction is generalized to the N-point amplitude in the manifestly dual manner suggested by Koba and Nielsen. We develop the operator formalism which exhibits the factorization property of the above amplitude. The related questions of ghost elimination and null states are discussed. Models with extra degrees of freedom and, in particular, the Neveu-Schwarz-Ramond model with spin, are treated. The latter model has a quark-line spectrum of mesons, but it possesses massless vector mesons and fermions. It is shown how the operator formalism is related to a quantized string. The theory of such a string is developed, with particular emphasis on the ghost-free “Coulomb-gauge” quantization. By constructing theories of interacting strings, we reproduce the dual-model S-matrix. A brief account is given of the theory of loops, in which one attempts to improve on the narrow-resonance model in a perturbative manner.     

Multi-sine-Gordon models

This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three, or more distinct topological sectors, with multiplicity one, two, three or more, respectively. The investigation takes advantage of the deformation procedure introduced in previous work, which is used to introduce the new models, and to study all the defect structures they may comprise.     

Accuracy of local field enhancement models: toward predictive models?

An accurate computation of field enhancement in the vicinity of metallic nanostructures is fundamental for the prediction of different physical phenomena such as SERS or fluorescence, and also for the design of nanostructures for specific applications. Several numerical models have been developed and are used to compute the field enhancement. Nevertheless, its evaluation can be very tedious and boring due to the plasmon resonance increasing the intensity level, and to the discontinuity of the field near the material edges. The behavior of commonly used computational codes is investigated in order to identify the convergence problems, and to propose some solutions to control the accuracy in the computation of the field enhancement. PACS 02.70.-c; 42.25.Gy; 61.46.+w     

Multilevel crystal plasticity models of single- and polycrystals. Direct models

The paper continues the review of works on the development and application of multiscale physical models to analyzing the behavior of single- and polycrystals under severe plastic deformation. Unlike mathematical models of plasticity, this class of models operates with meso- and microstructures of deformed material and allows analysis of their evolution. The recently much used so-called direct models that are based on crystal plasticity theories and numerical methods are discussed.