Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

Monte Carlo estimates of the SU(2) mass gap

Combining Monte Carlo and variational techniques, we compute the mass gap (or glueball mass) in the SU(2) lattice gauge theory. We obtain the estimate $\text{m}{}_{\mathrm{g}}\text{=(2.4 ± 0.6)}\text{K}\text{, K}$ being the string tension. We also discuss previous results derived by numerical or strong coupling methods and present Monte Carlo data on the second moment of the correlation length.     

String tension,gluebal masses and finite size effects in lattice SU(3)

We estimate the string tension by looking at Wilson loops and measuring the correlation between Wilson lines at g² = 1.0 for lattice SU(3). The bound $\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}\text{?0.0087 ± 0.0011}$ is larger than the previous results. The mass of the 0⁺⁺ glueball is also estimated. The finite size effects on these quantities are shown to be large by comparing results on a 6³ × 10 lattice with those on 9⁴ lattice.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

Wilson loops on 324 lattices and theSU(3) potential

Wilson loops are calculated on 32⁴ lattices in the coupling regime 6/g ²=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.     

Fractional charges and the renormalization group in theSU(4)×O(4) string model

We study the renormalization group equations of the gauge couplings in theSU(4)×O(4)～SU(4)×SU(2) _L ×SU(2_ _R string model, derived in the context of the free fermionic formulation of the four dimensional superstring. We calculate the effective string unification scale taking into account string threshold corrections and we consider the consequences of then _L andn _R fractionally charged states, sitting in the (1, 2, 1) and (1, 1, 2) representations correspondingly, of the gauge symmetry of the model. Some of these states become massive at a very high scale, when a number of singlet fields acquire vev's. However, many of them (the precise number depends on the specific choice of the flat direction) remain in the massless spectrum. We consider various cases and find that, for specific choices of flat directions, the physical parameters of the model, like the grand unification scale and the low energy parameters sin²θ _W and α₃, depend only on the differencen _?=n_L-n_R. We study more general cases where remnants of the exotic doublets remain below theSU(4) breaking scale. We also solve the coupled differential system of the renormalization group equations for the gauge and the Yukawa couplings and estimate the range of the top quark mass which is found to lie in the range 140 GeV<m _t<190GeV.     

Electric quadrupole and magnetic dipole moments of the first excited 2+ states of186Os and188Os

The spectroscopic quadrupole moments and the magnetic dipole moments of the lowest 2⁺ states in¹⁸⁶Os (137 keV) and¹⁸⁸Os (155 keV) have been determined by Mößbauer transmission experiments. The electric quadrupole momentsQ ₂₊(Os 186)=? (1.80±0.22) b andQ ₂₊(Os 188)=?(1.81±0.24) b as well as their ratioQ ₂₊(Os 188)/Q ₂₊(Os 186)=1.00±0.07 within the limits of error agree withB(E2) data, if a comparison on the basis of the rotational model is made. For the g-factors and their ratio g₂₊(Os 186)=0.281±0.008, g₂₊(Os 188)=0.305±0.015 andg ₂₊(Os 188)/g ₂₊(Os 186)=1.08±0.05 was obtained. All results are compared with recent model calculations.     

Low temperature ESR of K2Pt(CN)4Br0.3. 3.2 H2O

Electron spin resonance has been observed in high purity single crystals of K₂Pt(CN)₄Br_0.3·3.2H₂O, (KCP), in the temperature range of 4.22–80 K. Two types of paramagnetic species are found to dominate the spectrum. One of these is an inhomogeneously broadened line showing no resolved hyperfine splitting and having g_∥ = 1.946 ± 0.003 and g⊥ = 2.340 ± 0.003. The second paramagnet is identified as a Cu²⁺ impurity center with g_∥ = 2.231 ± 0.003, g⊥ = 2.079 ± 0.002 and hyperfine tensor A_∥ = 467 MHz, A_⊥ = 70 MHz.     

SU(2) string tension,glueball mass and interquark potential by Monte Carlo computations

Monte Carlo simulations of the SU(2) gauge system on a large (16⁴) lattice and with high statistics are performed to determine several quantities of physical interest. Previous evaluations of the ratio between string tension, σ, and scale constant, Λ₀, are confirmed. The mass of the glueball is found to be approximately 3√σ and the potential between static charges at very small separation is measured.     

Preparation and comparative structural properties of porous SnO2 microrods and submicrorods

A facile two-step approach has been used for the synthesis of porous SnO₂ rods: the initial room-temperature precipitation of precursor SnC₂O₄ and its subsequent thermal decomposition at 550 °C. Both the as-obtained porous SnO₂ microrods (length ～10.0?±?3.5 μm, diameter ～1.1?±?0.4 μm) and submicrorods (length ～5.8?±?1.9 μm, diameter ～0.4?±?0.1 μm) are the crystalline mixtures of major tetragonal and minor orthorhombic crystal phases, showing a tetragonal fraction of 84.7 and 87.0 %, respectively. When applied as a lithium-ion battery anode, the porous submicrorods (specific surface area ～13.6 m² g^?1) can deliver an initial discharge capacity of 1,730.7 mAh g^?1 with a high coulombic efficiency of 61.6 % and show the 50th discharge capacity of 662.8 mAh g^?1 at 160 mA g^?1 within a narrow potential range of 10.0 mV to 2.0 V. Similarly, even the anode of porous microrods (specific surface area ～11.8 m² g^?1) can still exhibit an initial discharge capacity of 1,661.1 mAh g^?1 at 160 mA g^?1 with a coulombic efficiency of 60.9 %. Regardless of the polymorphic nature, the acquired porosity may only alleviate the huge volume change of anodes for the first cycle; thus, the structural parameters of average size and specific surface area can be feasibly associated with the enhanced lithium storage capability. Anyway, these indicate a facile oxalate precursor method for the controlling synthesis and high performance of rodlike SnO₂ for lithium-ion batteries.     

Parity violations in electron-nucleon scattering and the SU(2)L ×SU(2)R ×U(1)L+R electroweak symmetry

The SU(2)_L ×SU(2)_R ×U(1)_L+R model of elecroweak interactions is described with the most general gauge couplings g_L, g_Randg_L+R. The case in which neutrino neutral current interactions are identical to the standard SU(2)_L ×U(1)_L+R model is discussed in detail. It is shown that with the weak angle lying in the experimental range sin²θ_w = 0.23 ± 0.015 and 1 < g_L²/g_R² < 3 it is possible to explain the amount of parity violation observed at SLAC and at the same time predict values of the “weak charge” in bismuth to lie in the range admitted by the controversal data from different experiments.     

Transient magnetic fieldg-factor measurements of 2 1 + in64, 66, 68, 70Zn

The implantation perturbed angular correlation technique (IMPAC) has been used to determine the magnetic dipole moments of the first excited 2⁺ states in the stable even-even Zn-isotopes. Transient magnetic field measurements for⁵⁶Fe in ferromagnetic Gd at 77 K have been performed for recoil velocities up tov/v ₀～8. The result confirms the earlier reported linear velocity dependence. Theg-factors are deduced to be 0.46±0.10, 0.47±0.11, 0.46±0.14 and 0.30±0.07 for^{64, 66, 68}Zn and⁷⁰Zn respectively. The results are compared with theoretical predictions.     

The anomalous quasi isotropic [g] tensor found for CdBr2:Ag2+ and AgBr0.15Cl0.85:Ag2+: An explanation through strong covalency

The “anomalous” quasi-isotropic [g] tensor observed in systems containing the elongated AgBr⁴⁻₆ unit (g_∥ = 2.078 ± 0.003; g⊥ = 2.065 ± 0.003) is reasonably explained, within a rigorous Molecular Orbital framework, in terms of a very high covalency, consistent with the optical electronegativity of Ag²⁺ and previous results on other Cu²⁺ and Ag²⁺ complexes. For the antibonding level 3b_1g(x² − y²) about 90% of the electronic charges should be on bromine ions. The present analysis reveals that g_∥ − g₀ is dominated by charge-transfer excitations while g_⊥− g₀ is dominated by crystal-field excitations.     

New evaluation of muon (g − 2) hadronic anomaly

The hadronic part a_H of the muon g-factor anomaly $\text{a ≡}\text{(g ? 2)}\text{2}$ is evaluated from latest data on σ(e⁺e^? → hadrons). For a p-wave ππ scattering length of a₁ = 0.04±0.005 we calculate a_H = (66±10) × 10^?9, compared to a(experiment) ? a(QED) = (60±29) × 10^?9. Half of the uncertainty on a_H is associated with the energy interval $\text{0.92 <}\text{s}\text{< 2}\text{GeV}$.     

Optical spectroscopy of Dysprosium Aluminum Garnet (DAG)

The absorption spectrum of antiferromagnetic dysprosium aluminium garnet (DAG) (T _N =2.50 °K) has been investigated at low temperatures. The groundstate splitting due to all interactions in the antiferromagnetic state is (5.27±0.10) cm^?1 extrapolated to 0 °K. The temperature dependence of the lineshift of the absorption lines is measured. Zeeman effect studies give theg-tensor of the groundstate asg _z =18.4±0.5,g _x =g _y =0.5±0.2. The studies also allow the determination of the critical fields asH _c ^[100] =(5.0±0.1) koe,H _c ^[111] =(3.9±0.2) koe andH _c ^[110] =(4.9±0.6) koe. In addition an investigation of a number of satellite lines is performed. Some of them can be interpreted as spin wave sidebands (Stokes and anti-Stokes); others obviously come from dysprosium ions which have impurity ions on regular lattice sites as neighbours.     

Magnetic moment measurements of the first-excited 2+ states in even Nd isotopes

The g-factors of the first-excited 2⁺ states of ^{144, 146, 148}Nd were deduced from precession measurements in which the excited nuclei recoil through (TF IMPAC) or stop in (IMPAC) magnetized iron. The transient and static hyperfine fields which are active in these cases have been calibrated. The results for the g-factors, combined with previous data which were reanalyzed in the present work, are: g₁₄₄ = 0.15 ± 0.02, g₁₄₆ = 0.25 ± 0.04, g₁₄₈ = 0.32 ± 0.04. The g-factor for ¹⁴⁴Nd, which is abnormally low for a collective 2⁺ state, cannot be accounted for theoretically.     

Electron paramagnetic resonance of Gd3 in YCl3·6H2O

The electron paramagnetic resonance spectrum of Gd³⁺ in YCl₃·6H₂0 with $\text{1}\text{100}$ dilution of Gd/Y ions, has been studied with an X-band spectrometer at 295, 77 and 1.77°K and with a K-band spectrometer at 295 and 77°K. The individual values of all the parameters are evaluated from the data at the three temperatures. In particular, the following values for the g-tensor and the zero-field splitting parameters b₂⁰ and b₂² are obtained from X-band data: at 295°K, g_zz = 1.994±0.005, g_xx = 1.992±0.005, g_yy = 1.997±0.005, b₂⁰ = 1.898 ±0.015 GHz, b₂² = ?2.247 ± 0.015GHz; at 77°K, g_zz = 1.999±0.008, g_xx = 2.000±0.008, b₂⁰= 1.978 ±0.022 GHz, b₂² = ?1.574±0.022GHz; at 1.77°K, g_zz = 2.002±0.010, g_xx = 1.990 ±0.010, b₂⁰ = 2.011 ± 0.025 GHz, b₂² = ?1.650 ±0.025 GHz. (The K-band values are found to be consistent with the X-band values). From the angular dependence of the data in the ZX plane (i) the angle X₀ which the Z axis makes with the a vector of the unit cell, is determined to be 58.00 ±0.25° and (ii) the existence of pseudo-symmetry axes at ±5° from the Z axis in the ZX plane as found by heat capacity and specific heat data has been confirmed. An estimate is also made of the extent of admixture of the excited ${}^6\text{P}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ state with the ground state ${}^8\text{S}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$.     

Experimental determination of the potential energy curves of the I(3/2u) and I(3/2g) states of Kr+ 2

The I(3/2u) and I(3/2g) states of Kr⁺ ₂ have been investigated by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy following (2 + 1′) resonance-enhanced multiphoton excitation via the 0⁺ _g Rydberg state located below the Kr?([4p]⁵5p[1/2]₀) + Kr(¹S₀) dissociation limit of Kr₂. From the positions of a large number of vibrational bands in the spectra of the ⁸⁴Kr₂ and ⁸⁴Kr-⁸⁶Kr isotopomers, the adiabatic ionization potentials (IP(I(3/2u)) = 112672.4 ± 0.8cm^?1, IP(I(3/2g)) = 111 395.0 ± 1.4cm^?1), the dissociation energies (D ⁺ ₀(I(3/2u)) = 368.8 ± 2.0cm^?1, D ⁺ ₀(I(3/2g)) = 1646.2 ± 2.3cm^?1) and vibrational constants for both ionic states have been determined. Potential energy curves have been extracted which perfectly reproduce all experimental observations and are accurate over a wide range of energies and internuclear distances. The equilibrium internuclear distances (R ⁺ _e(I(3/2u)) = 4.11 ± 0.04 Å, R ⁺ _e(I(3/2g)) = 3.35 ± 0.10 Å) have been derived by comparing the intensity distribution in the PFI-ZEKE photoelectron spectra to calculated Franck-Condon factors. The dissociation energy of the I(3/2g) state and the equilibrium internuclear distance of the I(3/2u) state differ markedly from previously reported values.     

Mode-crossing signals of high order on the 4d 95s 2 2 D 5/2 state of Cd II isotopes

In the linearly polarized radiation field of a 442 nm He-Cd laser containing a natural isotope mixture, saturation-induced mode-crossing signals of the 4d ⁹5s ^{2 2} _5/2 state of Cd II are observed due to the even as well as the odd isotopes. The signal width of about 10^?4 T yields high resolution. Thus the signal splitting respective to the magnetic quantum number can be resolved. Theg _J - andg _F -factors of the² D _5/2 state are determined as follows:g _J=1.1980±0.0036,g _F(F=2)=1.397±0.008,g _F(F=3)=1.002±0.009.     

The string tension of compact U(1) four-dimensional lattice gauge theory

Monte Carlo simulations of the string tension are calculated for four-dimensional U(1) gauge theory on a 6⁴ lattice. The string tension follows the result -1n(β/2) in the high temperature region and is zero for β > β_c, where β_c is the critical inverse temperature.