SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Abelian lattice gauge theories in 3 + 1 dimensions: The linked cluster approach

We use the linked cluster expansion methods of Nickel to derive strong couping series for Z_N abelian gauge theories. These new results together with corresponding estimates using the exact linked cluster expansion algorithm are analysed and compared with previously obtained results for U(1) lattice gauge theory in 3 + 1 dimensions. We confirm the phase structure of these theories as found by other techniques. The critical value of N at which the phase structure of Z_N alters is estimated to be N_C = 4.5 ± 0.2. In each case the string tension estimates using the ELCE algorithm are found to be stable in the presence of a roughening transition.     

Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g^?24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z₂ in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.     

On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Electron paramagnetic resonance of Dy3+ in cubic ZnSe and Tm3+ in hexagonal CdS single crystals

Electron paramagnetic resonance has been observed for Dy³⁺ in ZnSe and Tm³⁺ in CdS. For Dy³⁺ doped ZnSe, an isotropic spectrum was observed having well resolved hyperfine lines due to ¹⁶¹Dy and ¹⁶³Dy. The g value obtained was 6.577 ± 0.002 and ¹⁶¹A was 191 ± 1 × 10⁴ cm^?1 and ¹⁶³A was 265 ± 3 × 10^?4 cm^?1. The agreement of the observed g value to g(τ₆) = 6.667 and the point-charge calculations suggest that Dy³⁺ occupies an interstitial (II) site with no local charge compensation. For Tm³⁺ doped in hexagonal CdS, an axial spectrum consistent with g_⊥ = 0, g_∥ = 10.722 ± 0.007, D = 2.57 GHz (crystal field splitting) and ¹⁶⁹A = 1207 ± 5 × 10^?4cm^?1. The large g_∥ value indicates that the Tm ion exits in the trivalent state. This is in reasonable agreement with previous reports of the non-Kramer's state of Tm³⁺.     

Hadron mass calculations with Susskind and Wilson fermions in the fundamental-adjoint plane

We report the results of hadron mass calculations in the valence (quenched) approximation, on an 8³ × 16 lattice. For Wilson fermions with the standard Wilson action we find good agreement with results form the hopping parameter expansion on a 16⁴ lattice at β = 5.7, with only a small finite size effect in the anticipated direction. The proton-to-rho mass ration is however too high by 60% and the delta-proton mass difference is too small. We have repeated these calculations at two points of the same string tension in the plane of the fundamental and adjoint couplings, in an attempt to avoid the unphysical critical point there; within statistical errors the meson masses remain the same, there is an improvement in the delta-proton splitting and the proton mass decreases slightly, but not enough to produce agreement with experiment. The estimates of lines of constant string tension obtained as a preliminary to the mass calculation are in good agreement with weak coupling expansions at the larger β values and cross over towards strong coupling predictions around β = 5.7. Also, crude estimates reveal the disappearance of the specific heat peak as one moves away from the unphysical singularity. For Susskind fermions we find some measure of agreement with other results form a 10³ × 16 lattice, but large, apparently finite size, effects in the rho mass at low quark mass. Meson masses in lattice units disagree with the Wilson fermion results by as much as a factor of 2. This disagreement persists in the fundamental-adjoint plane, suggesting the importance of studying improved fermion actions. At β = 6.0, Wilson fermion results show clear finite size effects on the 8³ × 16 lattice.     

Plaquette expansion study of compact U(1) lattice gauge theory in (2 + 1) dimensions

The plaquette expansion is applied to compact U(1) lattice gauge theory in (2 + 1) dimensions to high order: 1/N ⁸ for the ground state energy density and 1/N ⁷ for the anti-symmetric or photon mass gap, where N is defined as the number of plaquettes. Evidence of scaling in the photon mass gap is observed for low order (≤ 1/N ⁴) for inverse coupling values β = 0. 7 to 1. 25 with scaling behaviour given by the weak-coupling formula: M ²/β = exp(-5. 01β + 5. 82) in good agreement with other studies. Higher order results appear to diverge from the scaling slope past the transition point portenting the prospect that the strong coupling trial state in this region gives vise to an asymtotic series in 1/N for the photon mass gap.     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

Roughening transition in lattice gauge theories in arbitrary dimension: (II). The groups Z3, U(1), SU(2), SU(3)

Strong coupling expansions for the string tension and other quantities in lattice gauge theories are computed in arbitrary dimension for the groups Z₃, U(1), SU(2), SU(3). This enables us to determine the location of the roughening transition, which seems to be group independent when measured in an appropriate variable. In four dimensions, the strong coupling expansion of string tension calculated up to fourteenth order for SU(2), and twelfth order for SU(3) agrees nicely with Monte Carlo data up to the roughening point.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Mössbauer study of Er3+ in ErH3 and YH3

The Mössbauer spectra of ¹⁶⁶Er in ErH₃ and YH₃ have been measured. Using and axial Hamiltonian, the electronic gyromagnetic rations for the ground state of Er³⁺ in YH₃ have been deduced: g| = 11.6 ± 0.1 and g⊥ = 4.4 ± 0.1. The analysis yields crystal field parameters which provide the correct λ₇ ground state with these g-values.     

Interface tension in the Polyakov loop model

The interface tension of the Polyakov loop model is calculated by Monte Carlo simulation. The form of the operator measuring the tension is derived from QCD in the strong coupling limit. The result is αa ³=0.0255±0.0003 in terms of the lattice constanta. The interface profile is also calculated and the spatial extent of the interface is estimated to be 10 lattice spacings. The result implies that the phase transition in the Polyakov loop model is of first order.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Magnetic hyperfine fields on 111Cd in the Pd1+xMnSb heusler alloys

The time-differential perturbed angular correlation technique has been used to measure the magnetic hyperfine fields (mhf) acting on ¹¹¹Cd impurity on the series of alloys Pd_1+xMnSb with 0 ? x ? 1. We observe three diffrent mhf's which for small values of x are of the order of +250, ?250 and ?150 kOe, decreasing slowly for larger values of x. These three fields are associated with ¹¹¹Cd occupying the sites of Mn, Sb and Pd, respectively. In addition, magnetization measurements on three of the allows (x = 0, 0.4 and 0.8) gave magnetic moments on the Mn atoms of 3.88 ± 0.08, 4.18 ± 0.08, (4.14 ± 0.08)_μB and Curie temperatures of 470 ± 2,422 ± 5 and (288 ± 2) K, respectively. Our results together with the existing data for mhf's on various 5sp elements in the Pd₂MnSb Heusler alloy are compared with the Blandin-Campbell model and show an agreement which is only qualitative.     

Infrared diode-laser spectrum of the CH3CN ν2 band: Analysis of local resonances with ν6±1 + 2ν8±2, ν4 + ν7±1 + ν8±1, ν4 + ν6±1, ν4 + ν7±1, and 2ν70 + ν8±1 states

Fifty-one sections of infrared diode-laser spectra of acetonitrile have been measured in the region from 2283.5 to 2235.7 cm^?1. About 450 transitions belonging to the ν₂ band have been assigned for K ≦ 7 and J ≦ 44. Anomalies found in the rotational structure have been proven to be due to five local resonances. Observed transition frequencies have been fitted by a least-squares method to a model which includes Fermi-type resonances (Δk = 0, Δ? = ± 3n) with ν₆^±1 + 2ν₈^±2 and ν₄ + ν₇^±1 + ν₈^±1 states, x, y-type Coriolis resonances (Δk = ±1, Δ? = ?3n ± 1) with ν₄ + ν₆^±1 and ν₄ + ν₇^±1 + ν₈^±1 states, and a centrifugal-distortion-type resonance (Δk = ±2, Δ? = ?3n ± 2) with a 2ν₇⁰ + ν₈^±1 state. The 11 × 11 dimensional energy matrix has been diagonalized in order to obtain the perturbed energy levels. The standard deviation for the fit is 1.075 × 10^?3 cm^?1. The molecular constants determined are also listed.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

EPR and Optical Absorption Study of Cr3+-Doped Dipotassium Tetrachloropalladate

X-band electron paramagnetic resonance (EPR) study of Cr³⁺-doped dipotassium tetrachloropalladate single crystal is done at liquid nitrogen temperature. EPR spectrum shows two sites. The spin-Hamiltonian parameters have been evaluated by employing hyperfine resonance lines observed in EPR spectra for different orientations of crystal in externally applied magnetic field. The values of spin-Hamiltonian and zero-field splitting (ZFS) parameters of Cr³⁺ ion-doped DTP for site I are: g _x  = 2.096 ± 0.002, g _y  = 2.167 ± 0.002, g _z  = 2.220 ± 0.002, D = (89 ± 2) × 10^?4 cm^?1, E = (16 ± 2) × 10^?4 cm^?1. EPR study indicates that Cr³⁺ ion enters the host lattice substitutionally replacing K⁺ ion and local site symmetry reduces to orthorhombic. Optical absorption spectra are recorded at room temperature. From the optical absorption study, the Racah parameters (B = 521 cm^?1, C = 2,861 cm^?1), cubic crystal field splitting parameter (Dq = 1,851 cm^?1) and nephelauxetic parameters (h = 2.06, k = 0.21) are determined. These parameters together with EPR data are used to discuss the nature of bonding in the crystal.