Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Quantum Monte Carlo study on the phase transition for a generalized two-dimensional staggered dimerized Heisenberg model

In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models,we study a generalized staggered dimer model named the J0-J1-J2 model,which corresponds to the staggered J-J ' model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and 0,respectively.Using the quantum Monte Carlo method,we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1 as a function of coupling ratio α=J2/J0.We extract all the critical values of the coupling ratio αc for these models,and we also obtain the critical exponents ν,β/ν,and η using different finite-size scaling anstz,.All these exponents are not consistent with the three-dimensional Heisenberg universality class,indicating some unconventional quantum ciritcial points in these models.     

镶嵌正方晶格上具有次近邻耦合作用Ising模型的临界性质

采用部分格点自旋消约变换,将镶嵌正方晶格上具有最近邻耦合作用K1和次近邻耦合作用K2的Ising模型变换成等效的具有最近邻、次近邻和四体耦合作用的正方Ising晶格.发现系统的临界点在(K1C,K2C)=(0.5125,0.2134),由此决定系统的临界温度,幷讨论了系统的普适性.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

Zero-range interaction in arbitrary dimensions and in the presence of external forces

We analyze zero-range interactions in arbitrary dimensions and in the presence of external forces in terms of non-local separable potentials. We show that in one-, two- and three-dimensional cases this approach is equivalent to the standard method with a renormalization operator. Our analysis indicates that the method of a projection operator is also useful for studying processes occurring under the influence of additional forces. As an example we present exact solutions for a particle interacting with a static electric field.     

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

A Blume-Capel spin glass with competing crystal-field interactions on a hierarchical lattice

Renormalization-group methods are used with a hierarchical lattice to model a Blume-Capel spin glass with annealed vacancies and competing crystal-field interactions. The strength of competing cross-link interactions is progressively increased as the effects, upon the phase diagrams, are investigated. A series of phase diagrams have been produced, sinks interpreted, and critical exponents calculated for higher order transitions.     

Lattice games without rational strategies

We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game whose set of winning positions does not have a rational generating function.