11500580
Renormalization-group analysis of layered sine-Gordon type models
Abstract We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner–Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two “normal”, massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J . Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the “mass corrections”. The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J → 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.
119118170
Interplay of fixed points in scalar models
We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent ν of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.
55685041
Infrared fixed point in quantum Einstein gravity
A bstractWe performed the renormalization group analysis of the quantum Einstein gravity in the deep infrared regime for different types of extensions of the model. It is shown that an attractive infrared point exists in the broken symmetric phase of the model. It is also shown that due to the Gaussian fixed point the IR critical exponent ν of the correlation length is 1/2. However, there exists a certain extension of the model which gives finite correlation length in the broken symmetric phase. It typically appears in case of models possessing a first order phase transitions as is demonstrated on the example of the scalar field theory with a Coleman-Weinberg potential.
85464497
Functional renormalization group for quantized anharmonic oscillator
Abstract Functional renormalization group methods formulated in the real-time formalism are applied to the O ( N ) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.
119203296
Degeneracy induced scaling of the correlation length for periodic models
Abstract The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz–Thouless type phase transition.
54892796
Critical exponents of the O(N) model in the infrared limit from functional renormalization
We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.
53550841
An octonionic formulation of the M-theory algebra
A bstractWe give an octonionic formulation of the N=1$$ \mathcal{N}=1 $$ supersymmetry algebra in D = 11, including all brane charges. We write this interms of a novel outer product, which takes a pair of elements of the division algebra A$$ \mathbb{A} $$ and returns a real linear operator on A$$ \mathbb{A} $$. More generally, with this product comes the power to rewrite any linear operation on ℝn$$ {\mathbb{R}}^n $$ (n =1, 2, 4, 8) in terms of multiplication in the n-dimensional division algebra A$$ \mathbb{A} $$. Finally, we consider the reinterpretation of the D =11 supersymmetry algebra as an octonionic algebra in D =4 and the truncation to division subalgebras.
10468219
High-accuracy Penning trap mass measurements with stored and cooled exotic ions
The technique of Penning trap mass spectrometry is briefly reviewed particularly in view of precision experiments on unstable nuclei, performed at different facilities worldwide. Selected examples of recent results emphasize the importance of high-precision mass measurements in various fields of physics.
120165522
Mass measurements on stable nuclides in the rare-earth region with the Penning-trap mass spectrometer TRIGA-TRAP
The masses of 15 stable nuclides in the rare-earth region have been measured with the Penning-trap mass spectrometer TRIGA-TRAP. This is the first series of absolute mass measurements linking these nuclides to the atomic-mass standard {sup 12}C. Previously, nuclear reaction studies almost exclusively determined the literature values of these masses in the Atomic-Mass Evaluation. The TRIGA-TRAP results show deviations on the order of 3-4 standard deviations from the latest published values of the Atomic-Mass Evaluation 2003 for some cases. However, the binding-energy differences that are important for nuclear structure studies have been confirmed and improved. The new masses are discussed in the context of valence proton-neutron interactions using double differences of binding energies, {delta}V{sub pn}(Z,N).
14807424
TRIGA-SPEC: A setup for mass spectrometry and laser spectroscopy at the research reactor TRIGA Mainz
Abstract The research reactor TRIGA Mainz is an ideal facility to provide neutron-rich nuclides with production rates sufficiently large for mass spectrometric and laser spectroscopic studies. Within the TRIGA-SPEC project, a Penning trap as well as a beamline for collinear laser spectroscopy are being installed. Several new developments will ensure high sensitivity of the trap setup enabling mass measurements even on a single ion. Besides neutron-rich fission products produced in the reactor, also heavy nuclides such as 235 U or 252 Cf can be investigated for the first time with an off-line ion source. The data provided by the mass measurements will be of interest for astrophysical calculations on the rapid neutron-capture process as well as for tests of mass models in the heavy-mass region. The laser spectroscopic measurements will yield model-independent information on nuclear ground-state properties such as nuclear moments and charge radii of neutron-rich nuclei of refractory elements far from stability. TRIGA-SPEC also serves as a test facility for mass and laser spectroscopic experiments at SHIPTRAP and the low-energy branch of the future GSI facility FAIR. This publication describes the experimental setup as well as its present status.
96561563
Measurements of ground-state properties for nuclear structure studies by precision mass and laser spectroscopy
Atomic physics techniques like Penning-trap and storage-ring mass spectrometry as well as laser spectroscopy have provided sensitive high-precision tools for detailed studies of nuclear ground-state properties far from the valley of ?-stability. Mass, moment and nuclear charge radius measurements in long isotopic and isotonic chains have allowed extraction of nuclear structure information such as halos, shell and subshell closures, the onset of deformation, and the coexistence of nuclear shapes at nearly degenerate energies. This review covers experimental precision techniques to study nuclear ground-state properties and some of the most recent results for nuclear structure studies.