相关论文: Evaluation of Spectral Zeta-Functions with the Ren…
We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees generally proliferate with increasing average degree, the…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
The bond-percolation properties of the Hanoi networks are analyzed with the renormalization group. Unlike scale-free networks, they are meant to provide an analytically tractable interpolation between finite dimensional, lattice-based…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…
We report in a series of papers two types of generalized Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. In this first part the symmetrical operation of half length bonds on translational invariant…
The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring…
We investigate the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar Sturm-Liouville operator associated with a fractal self-similar measure…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
We obtain analytical five-loop results for the renormalization group $\beta$-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of…
The irreversibility of the renormalization group flow is conjectured to be closely related to the concept of entropy. In this paper, the variation of eigenvalues of the Laplacian in the Polyakov action under the renormalization group flow…
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the Density Matrix Renormalization Group, and makes use of the distribution of multipartite entanglement…
We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.
We compare the results of renormalization-group and lattice studies for the properties of the electroweak phase transition. This comparison reveals the mechanisms that underlie the phenomenology of the phase transition.
In this paper, we explore the spectral measures of the Laplacian on Schreier graphs for several self-similar groups (the Grigorchuk, Lamplighter, and Hanoi groups) from the dynamical and algebro-geometric viewpoints. For these graphs,…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…