Modified action glueballs

The mass of the 0⁺ glueball in 4-dimensional lattice gauge theory with a mixed SU(2)-SO(3) action is obtained via Monte Carlo. We work in a region far from the critical end point in the phase diagram, with an action partly motivated by renormalization group flows in the Migdal-Kadanoff approximation. A large-N resummation of perturbation theory is used to show that the mass gap scales as predicted by the perturbative renormalization group. Independent of this, our results show that the ratio of the glueball mass to the square root of the string tension, obtained from a previous Monte Carlo, is a renormalization group invariant.     

The renormalization constants of QED in unitary approximation

A unitary approximation for the time-evolution operator given through the exponential representation is used to calculate the renormalization constants of QED. The results obtained by this method are the same as the renormalization group improvement of the usual perturbation series taking into account terms up to the second order ine.     

Renormalization of N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by N = 1 mass term

N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by mass terms are considered. It is proved that for N = 4 there are no ultraviolet divergences in the mass renormalization constants to all orders of perturbation theory. For N = 2 our two-loop calculations show that the charge and mass renormalization constants contain only one-loop divergences and are the same in this order. It is shown by direct calculation that mass terms can acquire finite quantum corrections starting from the two-loop approximation. The renormalization scheme dependence of N = 4 renormalization group functions is investigated. We have found that unlike renormalization schemes with minimal subtractions of divergences other renormalization schemes give a nonzero β-function. At nonzero masses the β-function in MOM schemes is not zero even at the one-loop level. In the massless case β≠0 beginning from the two-loop approximation.     

Potential-moving,Migdal's recursion formula,differential renormalization and duality

Migdal's original recursion formula is rederived as a low-temperature approximation by an isotropic type of potential-moving. For self-dual spin or gauge systems this transformation is shown to be differentiably conjugate to another one, which is obtained as a high-temperature approximation. The conjugation relation is established through the duality mapping.This explains the mechanism leading to some exact results obtained with Migdal's differential renormalization equation. The last equation is also explicitly rederived as the result of potential-moving approximations inspired by the methods of differential renormalization in real space.Some applications and extensions of the above results are finally considered in connection with an approach, which was recently proposed for systematically improving Migdal's approximation.     

Simulation of Neutron Reflection from the Surface of a Nanostructured Object in the Modified Kinematic Approximation

The applicability of the modified kinematic approximation for simulation of the specular reflection and the diffraction of a neutron beam from regularly ordered nanostructured objects on the surface and in the surface material layer is analyzed. The obtained results are compared with those of the real experiment and simulation of the distorted-wave Born approximation (DWBA). The influence of various factors on the obtained results is analyzed. These factors include the effect of neutron-wave refraction at the interfaces between media, the spectrometer-resolution function, and renormalization of the results for a nonspecular scattering signal based on data obtained for a specular channel. It is shown that, in many cases, it is possible to obtain rather good agreement with the experimental data and with the results of calculations using DWBA methods and of calculations using the Parratt algorithm.     

The renormalization group and the ϵ expansion

The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ? = 4?d is explained [d is the dimension of space (statistical mechanics) or space-time (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 1–8 provide a self-contained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 6–8 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 10–13 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 11–13 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions.     

Efficient approximation of the dynamics of one-dimensional quantum spin systems

In this Letter we show that an arbitrarily good approximation to the propagator e(itH) for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resources in n and the error epsilon and exponential resources in |t|. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal's time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.     

通过平均场处理的严格重正化群变换方法对Potts模型的应用

本文运用作者所发展的严格docimation- 平均场近似方法对Potts 模型的临界指数作了计算.所得结果与严格解符合得很好, 而与计算工作量相当的重正化群方法相比, 精确度大为提高。 关键词：     

A Renormalization Group Study of the Ising Model on a Triangular Lattice with Long-Range Interactions

The critical exponents of the triangular lattice Ising model with long-range interactions γ^-s are calculated by the real space renormalization group. Using the simplest Kadanoff blocks and the lowest approximation of cumulant expansion, it is shown that there exists a finite critical temperature when 4(1 - ㏑2/㏑3) < s < 4.     

Phase boundary of the square-lattice Ising antiferromagnet by real space renormalization group methods

The transition temperature of the square lattice Ising antiferromagnet at finite magnetic field is calculated by three different approximations within the real space renormalization group approach. The most refined approximation is an extension of Kadanoff's potential moving method to a larger cell-size. The results of this approximation are in good agreement with recent Monte Carlo simulations and the Müller-Hartmann/Zittartz conjecture for the phase boundary.     

SU(2)格点规范理论中的重夸克相互作用力及势的计算

本文用Monte Carlo方法对四维对称格点规范理论中具有较好标度性行为的单元格EXP作用量计算了重夸克-反夸克势。计算中利用了重整化群处理方法和SU(2)群的正二十面体子群近似。计算结果与维象的弦理论给出的库仑势加线性势的形式一致。 关键词：     

Neutralino mass matrix in the nonminimal supersymmetric Standard Model

We study in detail the neutralino mass matrix in the minimal extension of the minimal supersymmetric Standard Model. The model contains a Higgs singlet besides the two Higgs doublets of the minimal model. A number of limiting cases are considered wherein the neutralino mass spectrum can be analytically obtained. Based on these analytical results several useful approximation formulas for the neutralino masses are obtained. Using the constraints from the renormalization group analysis of the model, we obtain the spectrum numerically and study the dependence of the neutralino masses on the parameters of the model. We compare the results of the approximation formulas with the numerical results, and thereby establish the applicability of the these formulae in the different regions of the parameter space.     

Dirac operator spectrum in the linear σ model

The spectrum of the Dirac operator for the linear σ Model with quarks in the large N_c approximation is presented. The spectral density can be related to the chiral condensate which is obtained using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear correaction are recovered. The spectrum beyond the low energy regime is discussed.     

Magnon renormalization in disordered ferromagnets

The renormalization of the magnon energies in disordered, isotropic ferromagnets is investigated in the Hartree approximation. An expression equivalent to the Keffer-Loudon-Bloch renormalization factor is obtained by replacing products of normal mode expansion coefficients by their weighted sample averages. The results of self-consistent calculations of the renormalization factor and the magnetization are reported for dilute bond and amorphous ferromagnets.     

重整化群变换应用于U(1)规范理论的定量分析

在Migdal及Migdal-Kadanoff重整化群变换方案中,我们导出了U(1)格点规范理论的强耦合(高温)近似和弱耦合(低温)近似,同时还得到了包括中间耦合区的数值结果。上述结果与严格的强耦合展开、弱耦合展开以及Monte-Carlo模拟结果进行了比较。 关键词：     

The double logarithmic approximation of deep inelastic leptoproduction in the quasielastic region

We determine the asymptotic behavior of the deep inelastic leptoproduction structure functions in the quasielastic region z → 1 in the leading double logarithmic approximation of QCD. It is shown how the asymptotic behavior is related to the ON/OFF limit of the Sudakov form factor. The running coupling constant is incorporated by comparing the double logarithmic approximation with the solution of the renormalization group equation. We compare our result with various suggestions to improve the convergence of the perturbative expansion in the quasielastic region.     

Critical analaysis of transfer reaction models from a microscopic point of view

Based on the resonating group method, transfer reaction form factors are derived in distorted wave Born approximation. As a direct consequence of antisymmetrization, renormalization operators of relative motion in entrance and exit channels are automatically included. These operators, when used in the passive core approximation, change the conventional reduced width amplitudes into those advocated by Fliessbach. In the present paper, however, his results are derived in a way which avoids the problematic use of non-orthogonal intermediate states in the cluster transfer approximation. It is proposed to use the conventional reduced width amplitudes, together with proper renormalization kernels, in order to separate structure effects from reaction dynamics (energy dependence, absorption etc.) which determines the actual importance of the renormalization operators in entrance and exit channels.     

The non-perturbative renormalization group in the ordered phase

We study some analytical properties of the solutions of the non-perturbative renormalization group flow equations for a scalar field theory with Z₂ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility χ(M) at M=±M₀ (M₀ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we stress that these conditions are not satisfied by a sharp cut-off in dimensions of space d<4.By generalizing a method proposed earlier by Bonanno and Lacagnina [Nucl. Phys. B 693 (2004) 36] to any kind of cut-off we propose to solve numerically the renormalization group flow equations for the threshold functions rather than for the local potential. It yields an algorithm sufficiently robust and precise to extract universal as well as non-universal quantities from numerical experiments at any temperature, in particular at sub-critical temperatures in the ordered phase. Numerical results obtained for the φ⁴ potential with three different cut-off functions are reported and compared. The data confirm our theoretical predictions concerning the analytical behavior of χ(M) at M=±M₀.Fixed point solutions of the adimensioned renormalization group flow equations are also obtained in the same vein, that is by solving the fixed points equations and the associated eigenvalue problem for the threshold functions rather than for the potential. We report high precision data for the odd and even spectra of critical exponents for different cut-offs obtained in this way.     

Inclusion of retardation effects in the nonrelativistic treatment of the lamb shift

Summary The retardation effects are included in the nonrelativistic calculation of the Lamb shift, by using a method which exploits theO(4) symmetry of the nonrelativistic hydrogen atom. This method has been previously applied by Lieber to the treatment of the Lamb shift. However, in contrast to his calculations, no kind of dipole approximation, leading to the introduction of an inconsistent cut-off frequency, is used in our treatment. Apart from obtaining cut-off-independent results, the inclusion of retardation effects makes also possible the calculation of the spin-radiation-field Lamb-shift contribution (which vanishes in the dipole approximation). Furthermore, our unambiguous renormalization, consisting of removing the unobservable free-electron self-energy contribution from our expressions, leads to finite analytical and numerical results for the energy level (Lamb) shifts. The comparison of these results with those obtained in a nonrelativistic treatment by other authors shows that our results are in better agreement with the experiment.