共查询到20条相似文献,搜索用时 390 毫秒
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A real space renormalization group is formulated for continuum (off-lattice) percolation problems. It is applied to the system of overlapping discs with a variety of distributions of disc radii. Monte Carlo method is used for obtaining recursion relations. The results support universality: The Harris criterion seems to work for percolation. The position of the critical point shows stability against introducing a distribution in the disc radii.Supported in part by SFB 125 Aachen-Jülich-Köln 相似文献
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《Physics letters. A》1982,91(5):246-248
A quenched-correlated percolation system is studied by using the real-space renormalization group method. We chose the nearest-neighbour short-range order α as the correlation parameter. By treating the correlated probability self-consistently in terms of site occupation probability p and α, we found that, in two dimensions, there is only one nontrivial physical fixed point at random percolation and the correlation is an irrelevant parameter which always leads to the same universality. 相似文献
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T. C. Dorlas 《Communications in Mathematical Physics》1991,136(1):169-194
A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional, parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of aglobal critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using informatioin about the asymptotic renomralization behaviour. It turns out that the trivial fixed point gives rise to a twoparameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the application of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved.A part of the material here presented was used in the author's thesis 相似文献
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The influence of defects coupling linearly to the order parameter on the critical behaviour of structural phase transitions is studied. A continuum model for the statics and dynamics is introduced and is investigated by the renormalization group theory. If the defects are slow a central peak is found, the characteristic width of which is determined by the defects. Concerning the critical behaviour the dynamical model belongs to the same universality class as the one studied previously by Grinstein, MA, and Mazenko. The concentration dependence of the central peak response is discussed inside and outside the critical region. 相似文献
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In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field. Additionally to the universal scaling functions, several universal amplitude combinations are considered. We compare our results with those of a renormalization group approach. 相似文献
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We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice. 相似文献
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A. G. Hunt 《哲学杂志》2013,93(29):3409-3434
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Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect. 相似文献
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We present a family of exact fractals with a wide range of fractal and fracton dimensionalities. This includes the case of the fracton dimensionality of 2, which is critical for diffusion. This is achieved by adjusting the scaling factor as well as an internal geometrical parameter of the fractal. These fractals include the cases of finite and infinite ramification characterized by a ramification exponentp. The infinite ramification makes the problem of percolation on these lattices a nontrivial one. We give numerical evidence for a percolation transition on these fractals. This transition is tudied by a real-space renormalization group technique on lattices with fractal dimensionality ¯d between 1 and 2. The critical exponents for percolation depend strongly on the geometry of the fractals. 相似文献
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Rotureau J Michel N Nazarewicz W Płoszajczak M Dukelsky J 《Physical review letters》2006,97(11):110603
The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum. 相似文献
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Yu. A. Kosevich E. S. Syrkin D. A. Semagin A. M. Kosevich 《Journal of Experimental and Theoretical Physics》2000,90(6):974-978
Resonance scattering of a transverse sound wave by a planar defect in an elastic isotropic medium is studied in a wide range of values of the ratio of the damping length and the size of the region of localization of longitudinal oscillations. The transition between two limiting cases is described. The character of the transition is demonstrated by typical plots of the dependence of the reflection and transmission coefficients on the parameter relating the wavelength of the incident wave and the strength of the defect. It is shown that renormalization of total reflection into conventional dissipative passage occurs for values of this parameter below a certain critical value. 相似文献
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Herbert W. Hamber 《General Relativity and Gravitation》2009,41(4):817-876
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of
the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other
non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An underlying theme is the attempt
at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation
theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second
theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge
theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality
of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral
quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework
naturally leads to considering a weakly scale-dependent Newton’s constant, with a scaling violation parameter related to the
observed scaled cosmological constant (and not, as naively expected, to the Planck length).
Invited lecture presented at the conference “Quantum Gravity: Challenges and Perspectives”, Bad Honnef, 14–16 April 2008.
To appear in the proceedings edited by Hermann Nicolai. 相似文献
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V. V. Prudnikov P. V. Prudnikov I. A. Kalashnikov S. S. Tsirkin 《Journal of Experimental and Theoretical Physics》2008,106(6):1095-1101
The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ of the short time evolution of a system with an n-component order parameter is calculated within a dynamical dissipative model using the method of Σ-expansion in a three-loop approximation. Numerical values of θ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series. 相似文献
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We develop a three-parameter position-space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity (vector) percolation in two dimensions. To do this, we study site-bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb, respectively. The global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class, and possibly that of random (scalar) percolation. However, if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation, we find them to be very different (although the corresponding values of the correlation length exponent are the same). This indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal, which is consistent with some of the recent numerical simulations. 相似文献
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An equation describing the impurity transport in a percolation medium is obtained and the inferences drawn from this equation are analyzed based on the scale invariance concept. A determining part in this analysis is allowance for the sinks inherent in such media. At distances shorter than the correlation length, the particles are transferred in the regime of subdiffusion; at large distances, the concentration asymptotics exhibits a characteristic “tail” shape. In the medium occurring in the state above the percolation threshold, the impurity transport over time periods longer than the characteristic time related to the correlation length is well described by the classical equation with a renormalized diffusion coefficient. In this case, the concentration tail has a Gaussian shape at moderate distances and tends to subdiffusion asymptotics at very long distances. A relation is established between the factor determining renormalization of the diffusion coefficient and the factor determining a decrease in the number of active impurity particles at large times. 相似文献
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A. Donini V. Giménez G. Martinelli M. Talevi A. Vladikas 《The European Physical Journal C - Particles and Fields》1999,10(1):121-142
A general nonperturbative analysis of the renormalization properties of four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the nonperturbative
determination of the operator renormalization constants in the lattice regularization independent (RI or MOM) scheme. We also
discuss the determination of the finite lattice subtraction coefficients from Ward identities. We prove that, at large external
virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent
to that based on Ward identities, in the continuum and chiral limits. As a feasibility study of our method, we compute the
mixing matrix at several renormalization scales, for three values of the lattice coupling , using the Wilson and tree-level improved SW-Clover actions.
Received: 26 February 1999 / Published online: 15 July 1999 相似文献
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The Doebner–Goldin equation developed for describing the quantum dissipative dynamics of one-particle system is extended to be applicable to many-body system. Practical formula for non-interacting system is also provided both for the continuum space framework and for the tight-binding framework. We show simple numerical demonstrations on the wavepacket dynamics both under a harmonic potential and a saw-like potential. 相似文献
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Rahul SRIVASTAVA 《Pramana》2016,86(2):425-436
Starting with ‘high scale mixing unification’ hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for both Dirac and Majorana-type neutrinos. Following this hypothesis, the PMNS mixing parameters are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using MSSM renormalization group equations. For both types of neutrinos, the renormalization group evolution naturally results in a non-zero and small value of leptonic mixing angle ??13. One of the important predictions of this analysis is that, in both cases, the mixing angle ??23 turns out to be non-maximal for most of the parameter range. We also elaborate on the important differences between Dirac and Majorana neutrinos within our framework and how to experimentally distinguish between the two scenarios. Furthermore, for both cases, we also derive constraints on the allowed parameter range for the SUSY breaking and unification scales, for which this hypothesis works. The results can be tested by the present and future experiments. 相似文献