A study of the bulk phase transitions of the SU(2) lattice gauge theory with mixed action

Using the finite size scaling theory, we reexamine the nature of the bulk phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice gauge theory at β_A = 1.25 where previous finite size scaling investigations of the deconfinement phase transition showed it to be of first order for temporal lattices with four sites. Our simulations on N⁴ lattices with N = 6, 8, 10, 12 and 16 show an absence of a first order bulk phase transition. We find the discontinuity in the average plaquette to decrease approximately linearly with N. Correspondingly, the plaquette susceptibility grows a lot slower with the 4-volume of the lattice than expected from a first order bulk phase transition.     

Mass gap and universality for euclidean O(N) and CPN−1 models

From a suitably defined correlation function we evaluate the strong coupling expansion for the mass gap of an euclidean version of the O(N) models in 2D. Good agreement is found for N = 0, 1 and 2 with the known values of the critical temperature and for N ? 3 with the continuum mass gap as evaluated in an hamiltonian approach. Another test of universality based on the use of an asymmetric lattice also yields good results. An analogous discussion for the CP^N?1 models is performed.     

耦合常数小于1时SU(2)格点规范理论的质量隙及β函数计算

通过改变格点规范理论的作用量,我们把Monte Carlo计算的“窗口”移到了耦合常数小于1的区域。这就提供了在较弱耦合下作Monte Carlo计算的另一种途径。在3.9≤β≤4.7区域内,在10⁴格点上,我们计算了SU(2)规范的重整化群β函数及质量间隙,观察到类似于Wilson作用量的标度行为,估算出M≈(3.9±1.0)σ^1/2。 关键词：     

THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian with the ground state being exactly known is made.In the range 0≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory.     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LGT

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct continuum limit is made.In the range 1.3≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory and the results obtained by another Hamiltonian which does not possess correct continuum limit.     

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).     

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.     

Analytic approximations to hamiltonian lattice field theories: (I). Periodic gaussian model for U(1) theories

Periodic gaussian models are introduced for local and global U(1) invariant hamiltonian lattice field theories. The models coincide with standard lattice theories at weak coupling, but the leading non-perturbative contributions to wave functions and physical quantities are exactly calculable. Electric charges are confined and the mass gap is finite if correlations of an integer-valued magnetic field are of infinite range (d = 2 + 1 gauge model). Otherwise, for short-range correlations, the mass gap and the string tension vanish at weak coupling (QED, XY model, etc.)     

THE MC CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

By combining Monte Carlo method and variational method,we calculate the mass gap of SU(2) lattice gauge theory in 18*18 lattice of 2+1 dimensions by means of the icosaheral subgroup (Y120) using a hamiltonian of which the ground state is exactly known.In the range 0<1/g²,we obtain the results which are in good agreement with analytical calculation of SU(2) group.The scaling behaviour of mass gap am=2.3g² is confirmed.     

Partial cross sections for Rb− photodetachment in the region of the Rb(5p 2 P 1/2 3/2) thresholds and their analysis by multichannel quantum defect theory

A crossed ion-laser beam apparatus has been used to measure accurate relative total and partial cross sections for photodetachment from Rb^? ions with high photon energy resolution (0.1–0.6 cm^?1) in the region of the Rb(5p ² P _1/2,3/2) thresholds (photon energy range 16,350–16,820 cm^?1). Satisfactory fits to these data by multichannel quantum defect theory (MQDT) have been obtained, resulting in a reliable set of seven MQDT parameters. The electron angular distribution parameter for the Rb(5_s) channel was found to beβ(5s)=2, independent of photon energy. MQDT predicts a sharp, window-type variation of?(5s) around the minimum of the 5s-cross section below the Rb(5p ² P _1/2) threshold (where an accurate experimental measurement ofβ(5s) was not possible) and a similar behaviour ofβ(6s) in the case of Cs^?photodetachment below the Cs(6p ² P _1/2) threshold.     

Analytic approximations to Hamiltonian lattice field theories (II). The weak-coupling behavior of U(1) theories

It is shown that at weak coupling physical quantities in hamiltonian U(1) lattive gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d ? 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions.Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2+1 U(1) gauge theory confines electric charges at all non-vanishing coupling.     

Universal weak coupling limit in (2+1)-dimensionalSU(2) lattice gauge theory

Mass gaps and wave functions in (2+1)-dimensionalSU (2) lattice gauge theory (no quarks) are investigated. Starting with lattice Hamiltonians possessing exactly known ground states and the correct naive continuum limit, it is possible to reach the very deep weak-coupling region. Using variational approximation and rescaling all parameters with the help of the dimensionful coupling constantg ², we gain a formulation that is independent of the special choice of the Hamiltonian in the weak-coupling limit. The mass gap can be calculated and a kind of wave function for excited states obtained.     

Mössbauer studies of magnetic behavior of 3d-doped REBa2Cu3−x Fe x O7+δ (RE=Y,Er, Dy,Gd)

A Mössbauer study has been made on⁵⁷Fe ions substituted into the Cu(1) site of REBa₂Cu_3?x Fe _x O_7+δ (RE=Y, Er, Dy, Gd;x=0.15, 0.30). At low temperature, the iron atoms antiferromagnetically order with a transition temperature which is dependent on the Fe concentration. The temperature dependence of the magnetic subspectra representing Fe ions with various local oxygen environments in YBa₂Cu_3?x Fe _x O_7+δ and ErBa₂Cu_3?x Fe _x O_7+δ fit a 2D-Ising model with a ratio of the anisotropic exchange between the two directions on the order of 0.5–1.0(10^?3) for the Y-compounds and on the order of 1 for the Er-compounds. The magnitude of the local dopant magnetization is related to a short-range chemical order which determines the magnetic chain size and defines the correlation lengths. For the Y-compound, the order is quasi-1D with strong intrachain but very weak interchain coupling. For the Er-compounds, the magnetic coupling is Ising 2D. The strong fluctuation behavior expected in low dimensional systems above and belowT _N is observed via characteristic relaxation in the Mössbauer linewidth nearT _N. For both the Dy- and Gd-compounds, the magnetic order is 3D. The magnitude of the rare-earth magnetic moments appears to affect the character of the magnetic interaction in the Cu(1)-site. However, a Mössbauer effect measurement at¹⁵⁵Gd nuclei in GdBa₂Cu_2.85Fe_0.15O_7+δ (T _N(Fe)～14 K) shows paramagnetic behavior at 4.9 K.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

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.     

Particular cases of particle production in inelastic lepton (anti) lepton scattering

As in a previous paper we consider the inclusive reactions e+e→e+e+ anything in the two photon exchange approximation. We present the complete calculation of the differential cross section dσ/dW² for the production of a state of effective mass W and we give the expression for the total cross section. We apply this to the muon pair and the pseudoscalar meson (π⁰, η and η) productions.     

Superconductivity and ferromagnetism in the orthorhombic system (TbxLu1−x)RuB2

The pseudoternary orthorhombic system Tb_xLu_1?xRuB₂) (0 ? x ? 0.1 andx = 1.0) has been investigated by static magnetization, ac susceptibility and resistivity measurements down to 1.5 K. Superconductivity occurs for 0 ? x ? 0.1, while ferromagnetic order occurs for x = 1.0. For each sample studied, the Tb ion maintains a configurationally stable trivalent state. The initial linear depression of the superconducting transition temperature yields a coupling constant value N(0)Γ² between conduction electrons and magnetic Tb³⁺ moments of 3.5 x 10^-4 ev-atom-states/spin-direction.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.     

Alternative scaling hypothesis forSU(2) andSU(3) lattice gauge theories

High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ _c ≈2.47. ForSU(3) the data fit well to ν=1 andβ _c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.     

Paul阱中基态低能多离化Fen+(n=1—3)离子的存储及反应特性

利用垂直交叉的激光束在Paul阱中溅射固体铸铁（FeC）靶，产生了低能多电荷铁离子 Feⁿ⁺(n=1—3), 得到了Fe³⁺离子在本底气压为3.0×10^-7 Pa下的衰减速率（0.96 s^-1）以及在1.3×10^-5 Pa下和中性气体分子N₂的反应产物. 关键词： Paul阱 低能多离化离子 反应特性