Coupled Hamiltonians and three-dimensional short-range wetting transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate

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(y) representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d = 3 at critical and complete wetting, respectively, which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. Building on earlier work by Parry and Boulter we investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i(y) we show that arbitrary two-field models H[X₁,X₂] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set

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of Hamiltonians based on proper collective coordinates s(y) near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,

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]

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, in which the degree of coupling is controlled by an angle like variable δ^*, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility χ₁ is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalised critical amplitude θ in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.     

Yukawaon model in the quark sector and nearly tribimaximal neutrino mixing

For the purpose of deriving the observed nearly tribimaximal neutrino mixing, a possible yukawaon model in the quark sector is investigated. Five observable quantities (2 up-quark mass ratios and 3 neutrino mixing parameters sin²2θ_atm, tan²θ_solar and |U₁₃|) are excellently fitted by two parameters (one in the up-quark sector and another one in the right-handed Majorana neutrino sector).     

Subtle errors in αs determination using “corrected data” of energy-energy asymmetry

For the determination of α_s in the process of hadron production from electron-positron annihilation at 35 GeV, the complete second-order QCD calculation is used to study the corrections to the so-called “corrected data” of the asymmetry of the energy-energy correlation function (Asy). It is found that the correction in the values of α_s using the asymmetry method can be quite large while that for the new method, the planar triple energy correlation (PTC), is negligible.     

Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Möbius Strip

We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and Möbius strip using Yang–Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang–Baxter techniques and functional equations can be used to study the conformal spectra of more general exactly solvable lattice models in these topologies. The results rely on certain properties of the eigenvalues which are confirmed numerically.     

Spin waves,vortices, fermions,and duality in the Ising and Baxter models

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition, that the Z_p^? Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.     

On the thermodynamics of the random one-dimensional Ising chain in a transverse field

For three simple one-dimensional disordered models: (a) the Ising chain with random magnetic moments in a transverse field, (b) the Ising chain with random coupling constants in a transverse field, and (c) the X-Y model with a special type of disorder, the asymptotic equivalence in the thermodynamic limit is proved and some of its consequences are discussed. The spectral density of the finite chain for the model (a) is calculated by Dean's method for several representative cases and the presence of the local modes is indicated. The expressions for the initial susceptibilities for the models (a) and (b) are reviewed and (in two cases) the derivations are simplified.     

Computation of correlation functions of the two dimensional Ising model

The spin-spin and energy-energy correlation functions of the two dimensional Ising model are computer on the Creutz cellular automaton. From the data for the spin-spin correlation functions, the values of the critical exponents ν and η are obtained. They are in agreement with their theoretical values.     

Ising Models with Four Spin Interaction at Criticality

We consider two bidimensional Ising models coupled by an interaction quartic in the spins, like in the spin representation of the Eight vertex or the Ashkin-Teller model. By Renormalization Group methods we write a convergent perturbative expansion for the specific heat and for the energy-energy correlation up to the critical temperature. A form of nonuniversality is proved, in the sense that the critical behaviour is described in terms of critical indices which are non trivial functions of the coupling. The logarithmic singularity of the specific heat of the Ising model is removed or changed in a power law (with a non universal critical index) depending on the sign of the interaction.     

Critical surface of the ising model with first-neighbor,second-neighbor,and four-spin interactions

Exact values are obtained for the slopesK ₁ ^c (0, 0)/K ₂,K ₁ ^c (0, 0)/K ₄ of the critical surface of paramagnetic-ferromagnetic transitionsK ₁ ^c (K ₂,K ₄) for the two-dimensional Ising model on a square lattice with first-neighbor, second-neighbor, and four-spin couplingsK ₁,K ₂, andK ₄, respectively. The results are obtained using universality arguments to relate the slopes to known spin-spin correlation functions forK ₂=K ₄=0. The equivalence of different expressions for the slopes in terms of correlation functions yields sum rules for the divergent part of certain sums over the second-neighbor and four-spin energy-energy correlation functions.     

Liouville field theory coupled to a critical Ising model: non-perturbative analysis,duality and applications

Two different kinds of interactions between a $\text{Z}{}_{\mathrm{n}}$-parafermionic and a Liouville field theory are considered. For generic values of n, the effective central charges describing the UV behavior of both models are calculated in the Neveu–Schwarz sector. For n=2 exact vacuum expectation values of primary fields of the Liouville field theory, as well as the first descendent fields are proposed. For n=1, known results for sinh-Gordon and Bullough–Dodd models are recovered whereas for n=2, exact results for these two integrable coupled Ising–Liouville models are shown to exchange under a weak–strong coupling duality relation. In particular, exact relations between the parameters in the actions and the mass of the particles are obtained. At specific imaginary values of the coupling and n=2, we use previous results to obtain exact information about: (a) integrable coupled models like Ising–$\text{M}{}_{\mathrm{p/p\prime }}$, homogeneous sine-Gordon model SU(3)₂ or the Ising–XY model, (b) Neveu–Schwarz sector of the Φ₁₃ integrable perturbation of N=1 supersymmetric minimal models. Several non-perturbative checks are done, which support the exact results.     

Magnetische untersuchungen an mischkristallen der quasibinären legierungssysteme (Cd Te)1-x (Mn Te)x und (Sn Te)1-x (Mn Te)x

The magnetic susceptibility and magnetization are presented for polycrystalline samples of the alloy systems Cd_1-xMn_xTe 0 < x 0.1 and Sn_1-xMn_xTe 0 < 4 0.4. The magnetic measurements were performed between 2.3 K and 300 K in external magnetic fields up to 11 kOe. At sufficiently high temperatures the susceptibility can be described by a Curie-Weiss law. In the system Sn_1-xMn_xTe θ_p is positive. A linear dependence θ_p ∞ x was found with θ_p(0.4) = 49 K. In the series Cd_1-xMn_xTe θ_p changes sign. For θ < x < 0.04 θ_p is positive with a maximum θ_p ≈ 10 K at x = 0.02. In the region x #62; 0.04 θ_p becomes negative with θ_p = -35 K at x = 0.1. The effective spin value of manganese is S_eff #62; 5/2 for all the samples. The investigation was done to check the assumption that ferromagnetic coupling may exist in tellurides of manganese if the shortest distance d_MnMn is greater than 3.4 Å. This hypothesis has been stated. In the case θ_p #62; 0 the results are partly explained by the RKKY exchange coupling.     

Energy flow and energy correlations in deep inelastic scattering

We study two examples of infrared-safe quantities in deep inelastic scattering: the flow of energy in a given angular range and the energy-energy angular pattern. We derive expressions for these quantities in perturbative QCD, to order α_s, and show explicitly their infrared safety. Our formulas for the angular energy flow and the energy-energy angular pattern depend only on well-defined QCD factors and on the deep inelastic structure functions. To gauge whether or not these perturbative QCD results are applicable to present day data, we estimate in a simple model the effects of hadronization and primordial parton transverse momentum. In general these non-perturbative effects mask the resulting QCD pattern at present energies, but vanish more rapidly at higher energies than the QCD effects. However, we point out two examples where it may be possible to test the perturbative QCD predictions with available data. One of them involves studying the x-dependence of the azimuthal asymmetry of the energy flow. The other involves studying the angular width of the energy-energy correlation function.     

The Fe(α, γ)Ni reaction at excitation energies in the region of the giant dipole resonance

Excitation functions for the ⁵⁶Fe(α, γ₀)⁶⁰Ni and ⁵⁶Fe(α, γ₁)⁶⁰Ni reactions have been measured at 90° to the beam direction over the bombarding energy range 8.0–17.6 MeV. Gamma-ray angular distributions were measured at ten bombarding energies. Excitation functions for the ⁵⁹Co(p, γ₀)⁶⁰Ni and ⁵⁹Co(p, γ₁)⁶⁰Ni reactions were measured over the range E_x = 16.58–16.92 MeV and compared with the (α, γ) data. The angular distribution data indicate that the (α, γ₀) and (α,γ₁) reactions proceed through 1⁻, and 1⁻ and 3⁻ states, respectively. The (α, γ) excitation functions are discussed with respect to isospin splitting of the ⁶⁰Ni giant dipole resonance. The fine structure observed in the excitation functions is shown to be most probably due to Ericson fluctuations. The gross (α, γ) cross sections are shown to be in reasonable agreement with the results of calculations made using the theory of Hauser and Feshbach assuming excitation of the giant dipole resonance.     

Wess–Zumino Currents on S3 × R Spacetime

Based on the group theory powerful techniques, as a rigorous tool for treating fields on S ³ × R spacetime, which is the manifold of SU(2), we put the supersymmetric Wess–Zumino model on the S ³ × R background. After deriving the system of Klein–Gordon–Dirac-type equations, for the scalar and Majorana fields, we get in the corresponding current, besides the supercurrent, an additional term due to the coupling of spin to gravity. Finally, considerations on the solutions of the fields equations are made, pointing out significant differences from the Minkowskian case.     

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper''s operator

Harper's operator is the self-adjoint operator on defined by

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. We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bond on the norm of H_θ,: H_{θ,≤ 2(1 + √2 + cos(2πθ))}. We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H_θ, as the image of H_θ = U_θ + _θ^* + V_θ + V_θ^* in a suitable representation of the rotation algebra A_θ. We also use powers of H_θ to obtain various upper and lower bounds on H_θ = maxH_θ,. We show that “Fourier coefficients” of H_θ^k in A_θ have a combinatorial interpretation in terms of paths in the square lattice ². This allows us to give some applications to asymptotics of lattice paths combinatorics.     

The Susceptibility of the Square Lattice Ising Model: New Developments

We have made substantial advances in elucidating the properties of the susceptibility of the square lattice Ising model. We discuss its analyticity properties, certain closed form expressions for subsets of the coefficients, and give an algorithm of complexity O(N⁶) to determine its first N coefficients. As a result, we have generated and analyzed series with more than 300 terms in both the high- and low-temperature regime. We quantify the effect of irrelevant variables to the scaling-amplitude functions. In particular, we find and quantify the breakdown of simple scaling, in the absence of irrelevant scaling fields, arising first at order |T–T_c|^9/4, though high-low temperature symmetry is still preserved. At terms of order |T–T_c|^17/4 and beyond, this symmetry is no longer present. The short-distance terms are shown to have the form (T–T_c)^p (log |T–T_c|)^q with pq². Conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments.     

Conformal invariance and surface critical behavior

Conformal invariance constrains the form of correlation functions near a free surface. In two dimensions, for a wide class of models, it completely determines the correlation functions at the critical point, and yields the exact values of the surface critical exponents. They are related to the bulk exponents in a non-trivial way. For the Q-state Potts model (0 Q 4) we find η_<|; = 2/(3v − 1), and for the O(N) model (−2 N 2), η_<|; = (2v − 1)/(4v − 1).     

Consequences of relativity for the hyperfine interactions — with applications to transition metals

The strong influence of relativity on the hyperfine interaction is demonstrated by non-, scalar andfully relativistic calculations for solid transition metal systems. By calculations of hyperfine fields andof the nuclear spin lattice relaxation rate of Ag in Ag _x Pt_1–x it is shown that scalar relativistic calculations, which neglect the influence of spin-orbit coupling, seem to be sufficient to account for relativistic effects in many cases. To account properly for the symmetry-breaking caused by spin-orbit coupling, which is reflected by many hyperfine interaction properties, a fully relativistic approach is demanded. The corresponding formalism in the framework of the KKR-GF (Korringa-Kohn-Rostoker-Green's function) method of band structure calculation for magnetic solids is outlined. As applications results for the hyperfine fields of pure transition metals andalloys are presented.