A finite size scaling analysis of the O(4)-invariant lattice δ4 theory

The critical behaviour of the three- and four-dimensional N=4 vector model is investigated by means of a Monte Carlo simulation on lattices with size between 4³ and 16³, and between 4⁴ and 12⁴, respectively. For obtaining information about some critical properties of the model, we use a method due to Binder which is based on the theory of finite size scaling. For the three-dimensional model we get estimates of the critical exponents ν and η which are compatible with estimates obtained from the ϵ-expansion. In four dimensions we study for two different values of the bare self-coupling λ (λ=1 in our normalization, and λ=∞) the scaling behaviour of some Green function ratios at the phase boundary. In both cases we find compatibility with the “predicted” scaling behaviour at the gaussian fixed point. This is another independent numerical hint that the continuum limit of the four-dimensional O(4)-invariant lattice δ⁴-model is a free field theory.     

A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories

We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ? ₂ ⁴ and ? ₃ ⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

Wide Existence of the ΔI = 4 Bifurcation in the A～190 Superdeformed Bands

The superdeformed bands in A～190 region were systematically investigated to indicate the existence of ΔI = 4 bifurcation in this region. The behavior of bifurcation was also discussed.     

Nonzero θ13 for neutrino mixing in the context of A4 symmetry

In the original 2004 paper which first derived tribimaximal mixing in the context of A(4), i.e., the non-Abelian finite symmetry group of the tetrahedron, as its simplest application, it was also pointed out how θ(13) ≠ 0 may be accommodated. On the strength of the new T2K result that 0.03(0.04) ≤ sin(2)2θ(13) ≤ 0.28(0.34) for δ(CP) = 0 and normal (inverted) neutrino mass hierarchy, we perform a more detailed analysis of how this original idea may be realized in the context of A(4).     

A high-resolution infrared study of the ν4 band of CH3I

The infrared spectrum of the ν₄ band of CH₃I around 3060 cm⁻¹ was studied at a resolution of 5.4 × 10⁻³ cm⁻¹. About 1850 transitions were assigned. The K range was from KΔK = −7 to KΔK = +9 and the highest J values were about 75. The anomalous rotational structures observed in the subbands ^PQ₆ and ^RQ₅ – ^RQ₇ were explained as a consequence of Coriolis and Fermi resonances with combination levels. The standard deviation of the least-squares fit with 19 parameters was 0.00083 cm⁻¹. In addition to the fundamental band, the hot band ν₃ + ν₄ − ν₃ was also studied.     

A possible constructive approach to φ 4 4

We propose a constructive approach to ₄ ⁴ . It is based on formulating the ₄ ⁴ theory as an implicit function problem using multiplicative renormalization. For the corresponding lattice formulation we reduce the problem to verifying three conjectures. One conjecture is a regularity condition. The remaining two concern properties of the classical Ising ferromagnet, one of which we discuss in the frame work of critical point analysis.     

Analysis of the Effects of Three-nucleon Forces in A = 3, 4 Systems

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N ? d low energy scattering observables.     

A 300 µA Upgrade for the ISIS Accelerator

The Rutherford Appleton Laboratory (RAL) is home to the world's leading spallation neutron source ISIS [1]. The ISIS neutron producing target is driven by a 50 Hz, 800 MeV, 200 _A proton beam from a rapid cycling synchrotron, which is fed by a 70 MeV H_ drift tube linac (DTL) which in turn accepts beam from an H_ 665 keV Cockcroft-Walton preinjector. The ever increasing international demand for neutrons has motivated a bid to build a second target station at ISIS, for which £100 million funding has recently been approved by the U.K. government [2]. The second target station, operating at 10 Hz, will provide new scientific opportunities in soft condensed matter, biology and advanced materials.     

A possible constructive approach to ϕ 4 4 III

We continue our investigation into a constructive approach for _d ⁴ and prove under the hypotheses of our previous work that on a lattice and in the single phase region the theory is uniquely determined by the intermediate renormalization conditions. Then the Gaussian theory and the Ising model are the two extremal cases for all _d ⁴ theories.On leave of absence from the Freie Universität BerlinSupported in part by the Deutsche Forschungsgemeinschaft and by the National Science Foundation under Grant MPS 75-21212     

Some stereochemical criteria concerning the structural stability of A2BX4 compounds of type β-K2SO4

In A₂BX₄ structures which are isostructural to β-K₂SO₄ (with A being a monoatomic cation) there are two crystallographically independent cations surrounded by 11 and 9 X-atoms. The 11-coordinated cation is less firmly bound and the arrangement of its five closest neighbours is irregular. One of these contacts is approximately parallel to the pseudohexagonal axis of the structure and is often shorter than the sum of the corresponding ionic radii. A survey of available structural data indicates that the low-temperature structural instability of a good number of these compounds is related to the coordination of this 11-coordinated cation and especially to the bonding strength of this short bond, which is often the shortest cation-anion contact in the structure. Typically, the relative contribution of this contact to the bond-valence sum of the 11-coordinated cation is larger in the compounds which undergo phase transitions at lower temperatures. The presence of this short contact is correlated with the ratio of the lattice parameters a/b (Pnma-setting). In general, the Pnma phase is unstable at low temperatures in those compounds where this ratio is smaller. On the other hand, the value of a/b can be related to the ratio of the effective sizes of cations and BX₄ tetrahedra, so that typical low-temperature instabilities of the β-K₂SO₄ structure occur for smaller values of the ratio between cation radius and the sum of the ionic radii of atoms A and X. In most cases, the resulting phase transitions stabilize modulated structures (frequently incommensurate), with slight distortions with respect to the β-K₂SO₄ structure. However, when the bond valence sum of the eleven-coordinated cation is extremely low, more drastic (first-order) structural changes are observed (e.g. phase transitions into the Sr₂GeS₄ structure type). In addition, the survey indicates, especially in complex oxides, that low-temperature phase transitions are more probable in those structures with looser packing. Considering the criteria proposed, a set of compounds is indicated where low-temperature phase transitions are plausible.     

X-ray studies of the smectic B phase of the 4-bromobenzylidene-4′-alkoxyanilines

The results of X-ray studies of the nine members (4?÷?12) of the 4-bromobenzylidene-4′-alkyloxyaniline homologous series (nBBAA) in smectic B (SmB) and smectic A (SmA) phases are presented. Interestingly, no SmC phase was identified. The thickness of smectic layers in the SmA and SmB phases was estimated showing unexpectedly that in SmA it is bigger than in the SmB. For the SmB phase, orthorhombic unit cell parameters were determined as a function of temperature. The obtained data are discussed in relation to rotational dynamics.     

On the large order behavior of Φ 4 4

We continue the rigorous study of the large order behavior of the perturbation series for the ⁴ model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ₄ ⁴ is greater than or equal to the expected value given by the position of the first renormalon [2]. This result holds for any vector (²)² model withN components, and makes use of the Lipatov bound of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.     

A Search on the Klein-Gordon Equation

The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with two examples chosen specifically.     

A Lower Bound on the Entanglement in the Jaynes-Cummings Model

The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.     

A Lipatov bound for Φ 4 4 Euclidean field theory

We bound the large order behavior of these pieces of the renormalized perturbation expansion for ₄ ⁴ which do not contain renormalons [1]. The bound we obtain has the form of the leading asymptotic behavior computed by the Lipatov method, with the exact value of the Lipatov constant. Therefore, this paper is a step towards the rigorous study of the large order behavior of ₄ ⁴ and towards a proof of existence of the first renormalon singularity which should prevent the theory from being Borel summable. Using the results of this paper and the techniques of [15], one can for instance improve [17] the estimate [18] on the finiteness of the radius of convergence of the Borel transform of renormalized ₄ ⁴ and obtain that this radius is at least the exact value conjectured in [1].Supported in part by the National Science Foundation under Grant PHY 85-13554     

The non-trivial effective potential of the ‘trivial’ λΦ4 theory: A lattice test

The strong evidence for the triviality of (⁴)₄ theory is not incompatible with spontaneous symmetry breaking. Indeed, for a trivial theory the effective potential should be given exactly by the classical potential plus the free-field zero-point energy of the shifted field; i.e., by the one-loop effective potential. When this is renormalized in a simple, but nonperturbative way, one finds, self-consistently, that the shifted field does become non-interacting in the continuum limit. For a classically scale-invariant (CSI) ⁴ theory one finds m _h ² , predicting a 2.2 TeV Higgs boson. Here we extend our earlier work in three ways: (i) we discuss the analogy with the hard-sphere Bose gas; (ii) we extend the analysis from the CSI case to the general case; and (iii) we propose a test of the predicted shape of the effective potential that could be tested in a lattice simulation.     

A radio-tracer study of self-diffusion in the smectic phases iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate [IBPBAC]

Average translational self-diffusion coefficients, , have been determined in the smectic E, B and A phases of unaligned samples of iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate. A radiotracer technique was employed which was based on the serial sectioning method used in the study of diffusion in solids. In the smectic E phase is about 1 × 10^-14 m² s^-1. The self-diffusion in the smectic B phase fits reasonably well to an Arrhenius law with an activation enthalpy of 82 kJ mol^-1. The transition from the smectic B to A phase results in a dramatic rise in . In the smectic A phase the results fit an activation enthalpy for self-diffusion of about 168 kJ mol^-1. Similarities between the diffusion in the smectic E and B phases and in plastic solids are observed.