On the bifurcations occuring in the parameter space of the sixteen vertex model: I. Discrete bifurcations

The 16-dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points, i.e. points corresponding to models which possess extra symmetries not existing in nearby points. Equivalence classes of models having the same partition function are identified by means of a characteristic “normal” model, represented by a (4 x 4)-diagonal matrix N, and a pair of (2 x 2)-matrices A and B. In this paper the matrix N is assumed to be non-degenerate and the only bifurcations found are those associated with special types of matrices A and B, i.e. matrices whose decomposition in terms of Pauli-matrices corresponds to a vector a ≡ (a₁, a₂, a₃) or b ≡ (b₁, b₂, b₃) that is invariant with respect to one or more elements of the cubic symmetry group.The various bifurcation classes of models found include: a) the families of general- and “complementary” eight vertex models, b) discrete sets of doubly- and one-sided cyclic models and c) a number of secondary bifurcation classes within the eight-vertex families, among which is Baxters symmetric eight-vertex model.     

Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

We analyze unfoldings of a codimension two, steady-state/steady-state modal interaction possessing O(2) symmetry. At the degenerate bifurcation point there are two zero eigenvalues, each of multiplicity two. The spatial wavenumbers of the critical modes k_i are assumed to satisfy k₂ = 2k₁. We base our analysis on a detailed study of the third order truncation of the resulting equivariant normal form, which is a four-dimensional vector field. We find that heteroclinic cycles and modulated travelling waves exist for open sets of parameter values near the codimension two bifurcation point. We provide conditions on parameters which guarantee existence and uniqueness of such solutions and we investigate their stability types. We argue that such motions will be prevalent in continuum systems having the symmetry of translation and reflection with respect to one (or more) spatial directions.     

Canonical formulation of the spherically symmetric einstein-Yang-Mills-Higgs system for a general gauge group

The dynamics of the spherically symmetric system of gravitation interacting with scalar and Yang-Mills fields is presented in the context of the canonical formalism. The gauge group considered is a general (compact and semisimple) N parameter group. The scalar (Higgs) field transforms according to an unspecified M-dimensional orthogonal representation of the gauge group. The canonical formalism is based on Dirac's techniques for dealing with constrained hamiltonian systems. First the condition that the scalar and Yang-Mills fields and their conjugate momenta be spherically symmetric up to a gauge is formulated and solved for global gauge transformations, finding, in a general gauge, the explicit angular dependence of the fields and conjugate momenta. It is shown that if the gauge group does not admit a subgroup (locally) isomorphic to the rotation group, then the dynamical variables can only be manifestly spherically symmetric. If the opposite is the case, then the number of allowed degrees of freedom is connected to the angular momentum content of the adjoint representation of the gauge group. Once the suitable variables with explicit angular dependence have been obtained, a reduced action is derived by integrating away the angular coordinates. The canonical formulation of the problem is now based on dynamical variables depending only on an arbitrary radial coordinate r and an arbitrary time coordinate t. Besides the gravitational variables, the formalism now contains two pairs of N-vector variables (R, π_r), (Θ, π_Θ), corresponding to the allowed Yang-Mills degrees of freedom and one pair of M-vector variables, (h, π_h), associated with the original scalar field. The reduced Hamiltonian is invariant under a group of r-dependent gauge transformations such that R plays the role of the gauge field (transforming in the typically inhomogeneous way) and in terms of which the gauge covariant derivatives of Θ and h naturally appear. No derivatives of R appear in the Hamiltonian and the gauge freedom allows us to define a gauge in which R is zero. Also the r and t coordinates are fixed in a way consistent with the equations of motion. Some nontrivial static solutions are found. One of these solutions is given in closed form; it is singular and corresponds to a generalization of the singular solution found in the literature with different degrees of generality and the geometry is described by the Reissner-Nordström metric. The other solution is defined through its asymptotic behavior. It generalizes to curved space the finite energy solution discyssed by Julia and Zee in flat space.     

Non-supersymmetric vacua and the D-flatness condition

Some N = 1 gauge theories, including SQED and N_F = 1 SQCD, have the property that, for arbitrary superpotentials, all stationary points of the potential V = F + D are D-flat. For others, stationary points of V are complex gauge transformations of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.     

n-Dimensional complex riemann-einstein spaces with O(n−1, C) as the symmetry group

Working with a complex Riemannian space V_n, we determine the most general form of the metric which admits O(n?1, C) as a symmetry subgroup. The conformal curvature tensor, which is of type D for the real cross-section of signature (+---) with n = 4, has a very similar structure for n > 4 and complex V_n. Solutions of the empty space Einstein equations with the λ-term are then studied. There are two different static solutions which, with n = 4 and real cross-section of signature (+---), reduce to Schwarzschild-de Sitter metric, or to the Nariai's solution. A proof of a slight generalization of Birkhoff's theorem that every time-dependent solution of G_μv = λg_μv is reducible, by a coordinate transformation, to one of these two solutions, is given. The complete symmetry groups of the solutions obtained are examined. The techniques of embedding in a higher-dimensional flat space and of Kruskal's variables which exhibit the spurious nature of Schwarzschild's singularity are generalized to the case of (complex) n dimensions. General properties of geodesic lines for both solutions are examined and various real cross-sections of Nariai's solution for n = 4 are discussed. The last section studies some contractions of the two solutions.     

On the Meissner effect in gauge theories

The phase structure of spontaneously broken scalar electrodynamics in an external electromagnetic field is analyzed. With no external field, the spectrum comprises a scalar boson of mass m_H and a vector boson of mass m_W. If m_H ≤ m_W, it is shown that in the tree approximation, as the external field is increased, a first order phase transition to a restored symmetry phase occurs, and the critical field strength is calculated. Below the critical point the external field is completely screened, this being the analogue of the Meissner effect in superconductivity. If m_H > m_W, a third phase, characterized by vortex solutions of the field equations, occurs. Quantum effects, such as pair production in an electric field, are considered at the one (and two) loop level in the massless theory (the Coleman-Weinberg model). The leading correction to the critical magnetic field strength is calculated, and it is shown that for an external electric field the phase transition does not exist.     

Magnetoresistance of granular YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> HTSC in weak magnetic field: Angular dependence

The magnetoresistance of ceramic YBa₂Cu₃O_～6.5 HTSC samples is studied as a function of the mutual orientation of the current I and external magnetic field H _ext at T = 77.3 K in magnetic fields of up to ～500 Oe. It is found that, if the demagnetization factor D is taken into account, the effective critical field of complete penetration of Josephson vortices into weak links H _c2J ^eff does not depend on the mutual orientation of I and H _ext. The lower critical field H _c1A ^eff associated with the beginning of penetration of Abrikosov vortices into superconducting grains increases substantially with the angle between I and H _ext. The strongest variation with the mutual orientation of I and H _ext is exhibited by the critical field of the Bragg glass-vortex glass first-order phase transition H _BG-VG ^eff and by the magnetoresistance jump at this phase transition.     

Effective Mode Volume of Nanoscale Plasmon Cavities

The controlled squeezing of electromagnetic energy into nanometric volumes via surface plasmon-polariton excitations in plasmonic nanoresonators is analyzed using the concept of an effective electromagnetic mode volume V _eff, while taking careful account of the plasmon-polariton dispersion and the electromagnetic energy stored in the metal. Together with the quality factor Q of the cavity resonance, this enables a comparison with dielectric optical cavities, where V _eff is limited by diffraction. For a Fabry–Perot type planar metallic cavity, a one-dimensional analytic model as well as a three-dimensional finite-difference time-domain simulation reveal that V _eff is not bounded by diffraction, and that Q/V _eff increases for decreasing cavity size. In this picture, matter–plasmon interactions can be quantified in terms of Q and V _eff, and a resonant cavity model for the enhancement of spontaneous Raman scattering is presented.     

The field configurations of a static adjoint source in SU(2) lattice gauge theory

We study the spatial distribution and orientation of the colour fields around a static adjoint source using lattice gauge theory simulations in the pure gauge approximation. This configuration is not of immediate application to experiment although from a theoretical viewpoint it is the “hydrogen atom” of pure gauge QCD. We concentrate on the low-lying states of angular momentum J = 1 which are in the T₁₊ and T₁₋ representations of the cubic symmetry group. Sum rules relating integrals over the fields to the mass of the state are evaluated. The conclusion is that the colour fields are like those from a rough string rotating around the source.     

Inversion of the cyclotron resonance data in cadmium

The cyclotron resonance data for the third band lens in cadmium is inverted, using a spherical mapping procedure, to obtain a point for point value of the electron velocity |V_k| for different k points on the lens. The results are compared with the |V_k| deduced from an analysis of the magnetic surface states data.     

The electric fieldgradient at Cd-impurities in heavy rare earth metals

The static electric quadrupole interaction of¹¹¹Cd in the heavy rare metals Gd, Tb, Ho and Er has been studied at room temperature by time differential perturbed angular correlation techniques. From these measurements the effective electric field-gradient,V _zz ^eff , at the Cd-site was derived on a relative scale. The lattice contributions,V _zz ^lat , to the total electric fieldgradient have been determined by lattice-sum calculations. The ratioα=V _zz ^eff /V _zz ^lat , which to a certain extent represents the conduction electron contribution to the electric fieldgradient, decreases with increasing atomic number. Possible reasons for this behaviour are discussed.     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

On the stability of scalar-vacuum space-times

We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with arbitrary potentials V(ϕ), and in particular space-times with throats (including wormholes), which are possible if the scalar is phantom. At such a throat, the effective potential for perturbations V _eff has a positive pole (a potential wall) that prevents a complete perturbation analysis. We show that, generically, (i) V _eff has precisely the form required for regularization by the known S-deformation method, and (ii) a solution with the regularized potential leads to regular scalar field and metric perturbations of the initial configuration. The well-known conformal mappings make these results also applicable to scalar-tensor and f(R) theories of gravity. As a particular example, we prove the instability of all static solutions with both normal and phantom scalars and V(ϕ)≡0 under spherical perturbations. We thus confirm the previous results on the unstable nature of anti-Fisher wormholes and Fisher’s singular solution and prove the instability of other branches of these solutions including the anti-Fisher “cold black holes.”     

Natural vibration of unsymmetric cross-ply laminates

This study considers the linear vibration characteristics of square [0_n/90_n]_T laminates relative to their room-temperature static equilibrium configurations. A Rayleigh-Ritz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory.     

Spontaneous symmetry breaking in massless field theories,finite temperature and criticality

We study the behaviour at finite temperature of massless field theories exhibiting spontaneously broken solutions. We establish the occurence of a phase transition of the first kind at some critical point T_c which can be calculated to any finite order in perturbation theory. Similarly, perturbative methods can be used for thermodynamic functions in all regions, including the critical region. For the case of a gauge theory, we demonstrate the gauge independence of the critical point, the thermodynamic potentials and the order parameter to all orders of perturbation theory.     

Pressure induced superconductor quantum critical point in multi-band systems

In multi-band superconductors as inter-metallic systems and heavy fermions, external pressure can reduce the critical temperature and eventually destroy superconductivity driving these systems to the normal state. In many cases this transition is continuous and is associated with a superconducting quantum critical point (SQCP). In this work we study a two-band superconductor in the presence of hybridization V. This one-body mixing term is due to the overlap of the different wave-functions. It can be tuned by external pressure and turns out as an important control parameter to study the phase diagram and the nature of the phase transitions. We use a BCS approximation and include both inter- and intra-band attractive interactions. For negligible inter-band interactions, as hybridization (pressure) increases we find a SQCP separating a superconductor from a normal state at a critical value of the hybridization V_c. We obtain the behavior of the electronic specific heat close to the SQCP and the shape of the critical line as V approaches V_c.     

Correlations and static energies in the standard Higgs model

Correlations in the W-boson and Higgs boson channels and the static energy of an external SU(2) doublet charge pair are investigated by Monte Carlo calculations in the SU(2) lattice gauge theory with a scalar Higgs doublet field. The mass ratio m_W/m_H and the shape of the static potential are used to obtain information on the renormalization group trajectories in the three-dimensional coupling constant space. As a function of an appropriately chosen varibale, the measured quantities are, within errors, independent from the scalar self-coupling (λ) in a wide range 0.1 ⩽ λ ⩽ ∝. In the Higgs phase, a lower bound m_W/m_H ⩾ (1.0 ± 0.3) is obtained for the ratio of the Higgs boson mass to the W-boson mass.     

Two-loop free energy for finite temperatureSU(3) gauge theory in a constant external field

A two-loop calculation of the free energy for finite temperatureSU(3) gauge theory in an external fieldA ₀=const is carried out using background Feynman gauge. Nontrivial minima of the free energy are obtained atA ₀{gT forg→0 corresponding to the gauge symmetry breakingSU(3)→U(1)×U(1). Higher order perturbative effects are briefly discussed.     

Critical points and points of the bifurcation of the rotating magnetized newtonian polytropes with a 1 ⩽ n ⩽ 1.6 index

The presence of critical points and the bifurcation points of rotating Newtonian polytropes with an index of 1 ? n ? 1.6 has been shown for the first time in this paper. The symbolic-numerical calculation error in metric L ₂ has reached the size of the 10^?4 order. The approximate analytical solution to the problem to the abovementioned accuracy has been set forth. A critical value of the polytropes index n = n _k = 1.51025 has been calculated which is the highest among the critical points and bifurcation points. The value n _k corresponds to the infinitely slow polytropes rotation. Furthermore, in this paper the presence of the period jump at the bifurcation point T _b has been predicted and the relative value of this jump ΔT _b /T _b ～ B _0in ^4/3 has been estimated.