Related papers: Renormalization group treatment of rigidity percol…
We investigate the critical behavior that d-dimensional systems with short-range forces and a n-component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in a m-dimensional isotropic subspace of ${\mathbb…
We make an analysis of the two-dimensional U(1) lattice gauge theory with a $\theta$ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling…
This paper is the third in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. In this paper, we motivate and present a general approach…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two dimensional phase field crystal (PFC) model by a variety of renormalization group (RG) methods. We show that the presence of a…
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
The renormalization group is applied to the phi4 model in the symmetry broken phase in order to identify different scaling regimes. The new scaling laws reflect nonuniversal behavior at the phase transition. The extension of the analysis to…
Weakly correlated electrons on a square lattice are studied by angle-resolved functional renormalization group. Upon renormalization the interaction starts to depend on momenta and has pole-like solutions near a doping-dependent…
We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation…
When studying the collective motion of biological groups a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context,…
We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…
We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using low temperature perturbation theory. This type of transformations beyond $d=1$ is highly nontrivial even for free…
The Renormalization Group flow equations obtained by means of a proper time regulator are used to analyze the restoration of the discrete chiral symmetry at non-zero density and temperature in the Gross-Neveu model in d=2+1 dimensions. The…
A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle…