Percolation thresholds in two to six dimensions are studied by Monte Carlo methods in order to test Toulouse's recent conjecture that at six dimensions the Bethe lattice description of the threshold becomes exact. The results verify the existence of this critical dimensionality, but are only qualitatively in agreement with the predictions of expansions to $6-\epsilon$ dimensions.

A method of discriminating between rapidly moving electric and magnetic charges is proposed. The scheme relies on detection of the polarization of Cherenkov radiation.

We calculate the critical behavior of systems having a multicritical point of a new type, hereafter called a Lifshitz point, which separates ordered phases with $\overrightarrow{\mathrm{k}}=0\mathrm{}$ and $\overrightarrow{\mathrm{k}}\ne 0$ along the $\lambda$ line. For anisotropic systems, the correlation function is described in terms of four critical exponents, whereas for isotropic systems two exponents suffice. Critical exponents are calculated using an $\epsilon$-type expansion.

We consider phase transitions in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six.

We report an analysis of the Pioneer-10 data on Jupiter's magnetic field, in which the mass $\mu$ of the photon was treated as a free parameter. We set a limit of $\mu <~2\times {10}^{-11\mathrm{}} {\mathrm{cm}}^{-1\mathrm{}}\equiv 6\times {10}^{-16\mathrm{}} \mathrm{eV}\equiv 8\times {10}^{-49\mathrm{}} \mathrm{g}$. This is the smallest limit so far obtained from direct measurements. We compare our result with other published limits.

A method is developed which generates a class of nonlinear evolution equations in two and three spatial dimensions from an associated eigenvalue problem and its time dependence. Special cases include the equations describing nonlinear, resonantly interacting, wave envelopes in two and three dimensions; a "nonlinear Schrödinger" equation in two dimensions; and a two-dimensional analog of the Korteweg- de Vries equation.

A gauge theory for the Lorentz connection of a space-time describes geometries of stars with variable parametrized post-Newtonian parameter $\gamma$; its value depends explicitly on the structure of a star: The value of $\gamma$ for a neutron star is different from that for the solar system ($\left|{{\gamma }_{\odot }}^{-1\mathrm{}}\right|<~{10}^{-2\mathrm{}}$). Because of the absence of a "local parity invariance" $\gamma$ is positive for ordinary stars and $\gamma$ is negative for sources of gravity consisting of antimatter.

We have directly observed the sign reversal of the wave function of a fermion produced by its precession of $2\pi$ radians in a magnetic field using a neutron interferometer.

We first prove that $\Sigma \mathrm{}\left|e\right(V\left)\right|$, the sum of the negative energies of a single particle in a potential $V$, is bounded above by $\left(\frac{4}{15\pi }\right)\int {\mathrm{}\left|V\right|\mathrm{}}^{\frac{5}{2}}$. This, in turn, implies a lower bound for the kinetic energy of $N$ fermions of the form $\frac{3}{5}{\left(\frac{3\pi }{4}\right)}^{\frac{2}{3}}\int {\rho }^{\frac{5}{3}}$, where $\rho \mathrm{}\left(x\right)\mathrm{}$ is the one-particle density. From this, using the no-binding theorem of Thomas-Fermi theory, we present a short proof of the stability of matter with a reasonable constant for the bound.

The noise produced by thermodynamic fluctuations (e.g., in carrier number) is shown to diverge for ideal contact (spreading) resistors. For diffusion-controlled fluctuations the frequency spectrum is shown to be proportional to ${\omega }^{-1\mathrm{}}$ (i.e., $\frac{1}{f}$) for high frequencies. This behavior is shown to be approached by resistors whose surfaces have sharp corners. The relation to observed noise is briefly discussed.

We prove that the susceptibility of an isotropic, two-component, classical vector spin system, e.g., the rigid rotator, diverges in three or four dimensions as the magnetic field $h\to 0$, at all temperatures for which there is a spontaneous magnetization. The divergence is at least as strong as $h^{\frac{1}{2}}$ in three and as $\left|\ln h\right|$ in four dimensions. We also obtain bounds on the rates of exponential decay of the parallel- and transverse-pair correlation functions.

Conditions are given for the renormalization-group transformations of the Hamiltonian of a thermodynamic system which lead to a discontinuity in an order parameter.

We have made a high-sensitivity search with two calibrated detectors in coincidence for bursts of gravitational radiation at 710 Hz of duration < 0.1 sec. We find less than one event per day at a flux of 2 × ${10}^7$ ergs ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{Hz}}^{-1\mathrm{}}$.

We present high-temperature series through tenth order for the susceptibility of all classical scalar models with bilinear nearest-neighbor interactions in the absence of symmetry-breaking fields. As an example of the use of these results we examine the tricritical behavior of triple-well Landau-Wilson models which interpolate between the Blume-Capel and Riedel-Wegner models. The general series are given for the fcc, bcc, and simple cubic lattices.

The relation between the $s$-state Ashkin-Teller-Potts (ATP) model and the percolation problem given by Fortuin and Kasteleyn is used to formulate a renormalization-group treatment of the percolation problem. Both an $\epsilon$ expansion near 6 spatial dimensions and cluster approximations for the recursion relations of a triangular lattice are used. Series results for the ATP model are adapted to the percolation problem.

We present the results of gravitational radiation experiments with two 1400-kg antennas at ${\nu }_0=145\mathrm{}$ Hz. The square antennas, 1.65×1.65×0.19 ${\mathrm{m}}^3$, $Q_M\simeq 2.0\times {10}^5$, with electrostatic transducers of $\beta \simeq 1.8\times {10}^{-3\mathrm{}}$, have mean effective noise energy $\overline{D}\simeq 0.034k{T}_r$. The observed cross correlation of the outputs of the two detectors gives an upper limit for the relation between the mean energy spectrum density $F\left({\nu }_0\right)$ and the daily occurrence rate ${\dot{N}}_G$ of gravitational radiation pulses: $F\left({\nu }_0\right){{\dot{N}}_G}^{\frac{1}{2}}<~\left({3.6}_{-1.4\mathrm{}}^{+1.0\mathrm{}}\right)\times {10}^6$ J ${\mathrm{m}}^{-2\mathrm{}}$ ${\mathrm{Hz}}^{-1\mathrm{}}$ ${\mathrm{day}}^{-\mathrm{½}}$.

The behavior of the fixed-point Hamiltonian, $H^{*}$, and of the eigenoperators is derived for large values of the spatially uniform order parameter. When hyperscaling is valid the limit of $H^{*}$ is characterized by the exponent, $\delta$, but if hyperscaling is invalid this limit is Gaussian-like. Possible implications of these results, including the significance of marginal operators in approximate calculations, are discussed.

The Westerbork synthesis radio telescope was used to measure the solar gravitational deflection of radio waves over a period of 10 days, in October 1973, centered on the occultation of the quasar 3C279 by the sun. Simultaneous measurements at two frequencies (5.0 and 1.4 GHz) allowed the removal of the effects of refraction in the solar corona. The gravitational bending measured was 1.038±0.033 times that predicted by general relativity. As a by-product of these observations, values for the parameters at a model of the coronal electron density were also obtained.