Triviality of φ 4 4 and all that in a hierarchical model approximation

The infrared behavior of lattice _d ⁴ ,d 4, and dipole gases ind 1 is rigorously shown to be Gaussian within the context of a hierarchical approximation. Methods are developed to generalize the result beyond this approximation.On leave of absence from the Department of Mathematical Methods of Physics, University, 00-682 Warsaw, Hoza 74, Poland.     

A phase field model for vesicle–substrate adhesion

In this paper, a phase field model is developed for vesicle adhesion involving complex substrate and vesicle geometries. The model takes into account an adhesion potential that depends on the distance of vesicle to the substrate. A variational problem is solved in a 3D computational domain by minimizing the contribution of bending elastic energy and the adhesion energy under the constraints of total surface area and volume, described via a phase function. An adaptive finite element method is used to efficiently compute the numerical solutions of the model. The computational results are validated through comparison of several axisymmetric shapes with the sharp-interface ODE solution. Moreover, we compute shapes for non-axisymmetric situations to support the observation that concave substrates favor adhesion.     

Construction and Borel summability of infrared Φ 4 4 by a phase space expansion

We construct the thermodynamic limit of the critical (massless) ⁴ model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion. This expansion requires in a natural way the introduction of effective or running constants, and the infrared asymptotic freedom of the model, i.e. the decay of the running coupling constant, plays a crucial rôle. We prove also that the correlation functions of the model are the Borel sums of their perturbation expansion.     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

Λααα cluster model for the Λ 13 C nucleus

The _Λ ¹³ C hypernucleus is treated as a (1/2)⁺ bound state of the Λααα system. The s-wave model is used on the basis of differential equations for the corresponding Yakubovsky components. No account is taken of 2+2 clustering in the system. Phenomenological potentials are used to simulate the αα and αΛ interactions. The system as a whole is bound owing to the additional potential of three-body interaction between the alpha-particle clusters. The differential equations for the Yakubovsky components are solved numerically by the cluster-reduction method. The binding energies are calculated for the ground and the first excited state of the _Λ ¹³ C hypernucleus. It is shown that the dominant type of clustering in the system is (Λαα)α.     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

16O nucleus in the 4α cluster model

The ¹⁶O nucleus is treated as a bound state of the four-alpha-particle system showing 3α + α clustering. The pair interaction of the alpha particles involved is simulated by a phenomenological potential. Additional three-particle potentials are introduced in order that the entire system and its three-particle subsystems be bound. The parameters of these potentials are determined by fitting the experimental values of the binding energies and the root-mean-square radii of the ¹²C and ¹⁶O nuclei. The calculations are performed on the basis of the s-wave differential equations for the Faddeev and Yakubovsky components. The ground and the first excited state of the ¹⁶O nucleus are investigated. The most probable spatial arrangement of the alpha-particle clusters in the system is determined. The charge form factors are calculated for the ¹²C and ¹⁶O nuclei. The results of our model calculations comply well with experimental data.     

Shapes of growing droplets—A model of escape from a metastable phase

Nucleation from a metastable state is studied for an Ising ferromagnet with nearest and next nearest neighbor interaction and at very low temperatures. The typical escape path is shown to follow a sequence of configurations with a growing droplet of stable phase whose shape is determined by dynamical considerations and differs significantly from the equilibrium shape corresponding to the instantaneous volume.     

Renormalization of Dyson's hierarchical vector valued φ4 model at low temperatures

We investigate Dyson's hierarchical vector valued ⁴ model at low temperatures. The case is considered. The pure phase is constructed, and the existence of its large scale limit is proved. The limit is Gaussian, but an unusual normalization has to be chosen. In the direction of the spontaneous magnetization one has to divide by the square root of the volume, but in the orthogonal direction one has to divide by a different power of the volume for all low temperatures.     

Prediction for α3(Mz) in a string-inspired model

We apply the Renormalisation Group Evolution (RGE) to analyse the phenomenological implications of an extended supersymmetric model, for the value of the unification scale and the strong coupling at the electroweak scale. The model we consider is predicted to exist in Calabi–Yau string compactifications with Wilson line mechanism for E₆ symmetry breaking, contains additional matter beyond the MSSM spectrum and avoids the “doublet-triplet” splitting problem in the Higgs sector. The calculation is analytical in two-loop order and includes the effects of the heavy thresholds due to the additional matter considered. The value of α₃(M_z) can be brought within the experimental limits without a significant change of the unification scale from the MSSM prediction.     

A posteriori Brillouin—Wigner correction of limited multireference configuration interaction: analysis for an (H2)4 cluster model

An a posteriori Brillouin—Wigner correction is applied to a limited multireference configuration interaction study of a simple model problem consisting of four H₂ molecules arranged in a distorted octagonal conformation in which the degree of quasidegeneracy depends on a single parameter designated a. Double reference configuration interaction calculations are performed as a function of the parameter a. A posteriori Brillouin—Wigner corrections are applied and compared with a generalization of the Davidson correction for multireference applications. The calculated total energies for the ground state are compared with full configuration interaction studies carried out within the same basis set of Gaussian-type functions. The basis set dependence of the problem is explored by performing calculations in two small Gaussian basis sets: one of minimum basis set quality and the other of ‘double ζ’ type.     

Uniqueness of Gibbs states for generalP(ϕ)2-weak coupling models by cluster expansion

We consider quantum fields with weak coupling in two space-time dimensions. We prove that the set of their ultraregular Gibbs states consists of only one point and this point is an extremal Gibbs state.     

Hyper-radial adiabatic expansion for a muonic molecule dtμ

By using the hyper-radius, adiabatic potential energy curves with correct asymptotic energies are obtained for the Coulomb three-body problem. The bound state energies of the muonic molecules dtμ with total angular momentum J=0 calculated adopting the three lowest adiabatic potential energy curves are −318.72 and −34.36 eV for vibrational quantum numbers ν=0 and 1, respectively.     

Can the eigenstates of a many-body Hamiltonian be represented exactly using a general two-body cluster expansion?

It is proved that a recent conjecture that the exact ground-state wave function of an arbitrary many-fermion system with one- and two-body interactions may be represented by an exponential cluster expansion employing finite two-body operators, starting from any reference function sufficiently close to the exact eigenfunction, is not valid. We show that the space of initial reference functions which lead to the exact ground state is of dimension equal to the number of two-body operators. If the dimension of the multiparticle space is greater than the number of two-body operators, then the space of good reference functions is of measure zero in it.     

A pressure calibration method for a portable wide-access ＂panoramic＂ cell

A simple and convenient pressure calibration method is developed for a newly designed portable wide-access ＇panoramic＇ cell. This cell is adapted to angle-dispersive-mode high-pressure in situ neutron diffraction of reactor neutron sources. This pressure calibration method has established a relationship between the cell pressure and the anvil displace- ment （gasket compression） based on the fixed-point calibration technique. By employing TiZr gasket with a thickness of 3 mm and WC anvil with a culet of 4 mm diameter, the average anvil displacements are 1.31 mm and 2.22 mm for Bi phase transitions （2.55 GPa and 7.7 GPa）, and 1.85 mm for Ba phase transitions （5.5 GPa）, respectively. In this pressure range, the pressure increases quickly with decreasing gasket thickness, and undergoes a linear increase with the anvil displacement. By extrapolating the calibration curve, the cell pressure will achieve 10 GPa when the anvil displacement is around 2.5 ram.     

Is a Griffiths phase a prerequisite for colossal magnetoresistance?

Detailed measurements of the magnetic and transport behavior of the two La(1-x)Ca(x)MnO(3) single crystals exhibiting colossal magnetoresistance are summarized. The x=0.21 sample exhibits unusual exponents (delta = 20+/-1, gamma = 1.71+/-0.1, beta = 0.09+/-0.01, T(C) = 182+/-1 K) and, more importantly, a Griffiths phase characterized by an exponent lambda = 0.70+/-0.2. By contrast, the x=0.20 specimen displays Heisenberg model behavior with no evidence of such a phase. Thus while a Griffiths phase accounts for the behavior of La(1-x)Ca(x)MnO(3) near optimal doping, it does not appear to be a prerequisite for colossal magnetoresistance in this system.     

A multi-purpose phase modulator for one beam ESPI

This paper proposes a simple, compact, practical, less nonlinear, less decorrelation and multi-purpose phase modulator for one beam ESPI which can be used perform both phase shifting and fringe carriering techniques. Theory together with experimental demonstrations are presented.     

A multi-purpose phase modulator for one beam ESPI

This paper proposes a simple, compact, practical, less nonlinear, less decorrelation and multi-purpose phase modulator for one beam ESPI which can be used perform both phase shifting and fringe carriering techniques. Theory together with experimental demonstrations are presented.