相关论文: Branched Polymers and Percolation

We find that 2-dimensional (2-D) critical branched polymers with no impurities conclusively belong to the same universality class as 2-D random percolation clusters, although pure critical 3-D branched polymers do not belong to the 3-D…

We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…

Building on and from the work of Brydges and Imbrie, we give an elementary calculation of the volume of the space of branched polymers of order $n$ in the plane and in 3-space. Our development reveals some more general identities, and…

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions…

We propose a classification of critical behaviours of branched polymers for arbitrary topology. We show that in an appropriately defined double scaling limit the singular part of the partition function is universal. We calculate this…

In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…

We show that correlation functions for branched polymers correspond to those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves, as has been widely believed. In particular, the two-point function…

A nano-second scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as…

This article will review recent results on dimensional reduction for branched polymers, and discuss implications for critical phenomena. Parisi and Sourlas argued in 1981 that branched polymers fall into the universality class of the…

We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the…

Percolation phenomena of homopolymer brushes on a planar substrate are simulated using the molecular Monte Carlo method in 3 dimensions. The grafted polymers are isolated from each other at extremely low grafting density, whereas a…

We define a class of random matrix ensembles that pertain to random looped polymers. Such random looped polymers are a possible model for bio-polymers such as chromatin in the cell nucleus. It is shown that the distribution of the largest…

We use a recently developed lattice model to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long semiflexible chain. We study the effects of the…

We consider the simplest representative of the class of multiply branched polymer macromolecules, known as a pom-pom structure. The molecule consists of a backbone linear chain terminated by two branching points with functionalities…

Mitra et al. [Phys. Rev. E 99 (2019) 012117] proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But the conclusion is…

A directed polymer is allowed to branch, with configurations determined by global energy optimization and disorder. A finite size scaling analysis in 2D shows that, if disorder makes branching more and more favorable, a critical transition…

Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…

We point out some misconceptions in a recent paper by H. Aoki et al. [hep-th/9909060]. In particular, the claim that the two-point function of branched polymers behaves as 1/p^4 instead of 1/p^2 for large p is mistaken and in no way a…

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and…