Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

Entanglement in Spin-1/2 Dimerized Heisenberg Systems

We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of ground-state pairwise entanglement for the four-qubit model by identifying a Z₂ symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of the nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.     

Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2+ Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the perturbation formulas of g_i factors and hyperfine structure constants A_i based on the cluster approach for 3d⁷ ions in cubic, tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients F_ij (F₁₁, F₁₂, F₄₄), Z_ij (Z₁₁, Z₁₂, Z₄₄) and also g factor and hyperfine constant A for MgO:Co²⁺ are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values. The difficulty in explaining the coefficients F_ij and Z_ij is therefore removed.     

ISING-GAUGE ISING-HIGGS SYSTEM IN TWO DIMENSIONS

A brief review for Refs.[1] and [2] is presented.Z₂-gauge and Z₂-Higgs action on 2-dimen-sional lattice is given in terms of standard procedures.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z₂ topological indices. According to the Z₂ topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

Gravity with Electromagnetism on M4 × Z2

In the framework of the differential calculus on discrete group, which is a realization of noncommu tative geometry, we present a Kaluza-Klein-type unified Einstein-Maxwell theory on M⁴ × Z₂. By generalizing the usual concept ofi vielbein and connection and from the generalized torsion-free condition, we obtain a gravity theory which contains tensors, vectors and scafar field.     

M-Theory Inspired Low Energy Phenomenology

In both the scalar quasi-massless SUSY breaking scenario and dilaton-dominant SUSY breaking scenario, we analyze experimental constraints to the parameter space in M theory compactified on S¹/Z₂. The sparticle spectrum and some phenomenological predictions are given.     

Exotic Hadrons and Underlying Z2,3 Symmetries

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z₂ and Z₃ symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of  _n affine Lie algebras. It has been shown that Z_2,3 invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.     

The Standard Model with Higgs as Gauge Field on Fourth Homotopy Group

Based upon a fundamental principle, the generalized gauge principle, we construct a general model with G_L×G'_R×Z₂ gauge symmetry, where Z₂ = π₄(G_L) is the fourth homotopy group of the gauge group G_L, by means of the non-commutative differential geometry and reformulating the standard model with the Higgs field being a gauge field on the fourth homotopy group of their gauge groups. We show that in this approach not only the Higgs field is automatically introduced on an equal footing with ordinary Yang-Mills gauge potentials and there are no extra constraints among the parameters at the tree level but also most importantly the models survive quantum corrections.     

MONTE CARL0 SIMULATION OF 3-d LATTICE Z4 GAUGE-Z2 HIGGS THEORY

Phase diagram for 3-dimensional lattice Z₄ gauge-Z₂ Hiygs coupling system is constructed using Monte Carlo method (heat-bath method). The resulb are in agreement with the features predicted by Fradkin and shenker_[1]. To find accurate positions of the transition points we proposed a method of thermal cycles recooling near the transition points.     

Z2-Symmetry Restoration in the λΦ4 Field Theory with Normal-Ordering Renormalization

Using the Gaussian wavefunctional approach plus normal-ordering renormalization, we show that for the λΦ⁴ field theory, the discrete Z₂-symmetry broken at the classical level is restored within some parameter region not only in (1+1) dimensions but also in (2+1) and (3+1) dimensions.     

Null Geodesics in Brane World Scenarios

We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z₂ symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate the Z₂ symmetry.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Projection Operator on Rational Noncommutative OrbifoldT2/Z4

In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator \hat{P} on the rational noncommutative orbifold T²/Z₄. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.     

Topological phase transition in a ladder of the dimerized Kitaev superconductor chains

We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains.The topological class of the system is determined by the relative phase θ between the inter-and intra-chain superconducting pairing.One topological class is the class BDI characterized by the Z index,and the other is the class D characterized by the Z_2 index.For the two different topological classes,the topological phase diagrams of the system are presented by calculating two different topological numbers,i.e.,the Z index winding number W and the Z_2 index Majorana number M,respectively.In the case of θ=0,the topological class belongs to the class BDI,multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed.In the case of θ = π/2 it belongs to the class D.Our results show that for the given value of dimerization,the topologically nontrivial and trivial phases alternate with the variation of chemical potential.     

Photothermal imaging by F–Z2 colour centre conversion in KCl doped with gadolinium

A new scheme for photonic information storage based on photothermal F to Z₂ colour centre conversion is presented. Z₂ centres are formed by F-band bleaching in the temperature range 300 to 500 K in additively coloured crystals of KCl doped with gadolinium. The variation of the optical density in the F-band is studied as a function of the logarithm of exposure in order to obtain the Hurter-Driffield characteristics of the storage medium. The ideal parameters of storage are arrived at and the writing sensitivity of the medium for the proposed process is determined. Photonic information storage using a helium-neon laser is demonstrated and the results are compared with other reported schemes.     

The Duality Transformation for an n-Species Ising Model Interacting with Z2 Gauge Fields on a Random Surface

The duality transformation is carried out for an n-species Ising spin system interacting with Z₂ gauge fields. For n > 1, we find that the dual model has topological terms when the surface is topologically nontrivial. The plaquette interaction of the gauge fields is dual to an n-spin coupling in the dual model.     

Phase Transitions of a Dilute O(n) Model

We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix. Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point, the tricritical line extends to the n=2 point describing a tricritical O(2) model.     

Monte Carlo Study of 3-d Z4 Gauge-Z2 Higgs Theory with Radial Degree of Freedom

Phase structure of the 3-d lattice Z₄ gauge-Z₂ Higgs theory is investigated by the Monte Carlo simulation. We find a new phase, named Higgs Ⅱ phaae, when λ (scalar self-coupling constant) is small. It is a result of the radial excitation of Higgs field.     

Excited TBA equations II: massless flow from tricritical to critical Ising model

We consider the massless tricritical Ising model perturbed by the thermal operator _1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A₄ lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.