Related papers: Finite scale singularity in the renormalization gr…
We study the surface critical behavior of semi-infinite systems belonging to the bulk universality class of the Ising model. Special attention is paid to the local behavior of experimentally relevant quantities such as the order parameter…
We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
Rigidity transitions induced by the formation of system-spanning disordered rigid clusters, like the jamming transition, can be well-described in most physically relevant dimensions by mean-field theories. A dynamical mean-field theory…
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially…
We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not…
We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E, 66 045101(R) (2002)], the critical point moment ratios of…
Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…
The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is…
In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these…
We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that…
The critical dynamics of model C in the presence of disorder is considered. It is known that in the asymptotics a conserved secondary density decouples from the nonconserved order parameter for disordered systems. However couplings between…
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
We briefly summarize some recent theoretical developments in perturbative QCD, emphasizing new ideas which have led to widening the domain of applicability of perturbation theory. In particular, it is now possible to calculate efficiently…
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…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…