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Register a new userPhase separation transition of reconstituting k-mers in one dimension
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Pradeep Kumar Mohanty
Publication date
2014
fields
Physics
and research's language is
English
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We introduce a driven diffusive model involving poly-dispersed hard k-mers on a one dimensional periodic ring and investigate the possibility of phase separation transition in such systems. The dynamics consists of a size dependent directional drive and reconstitution of k-mers. The reconstitution dynamics constrained to occur among consecutive immobile k-mers allows them to change their size while keeping the total number of k-mers and the volume occupied by them conserved. We show by mapping the model to a two species misanthrope process that its steady state has a factorized form. Along with a fluid phase, the interplay of drift and reconstitution can generate a macroscopic k-mer, or a slow moving k-mer with a macroscopic void in front of it, or both. We demonstrate this phenomenon for some specific choice of drift and reconstitution rates and provide exact phase boundaries which separate the four phases.
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Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of $k times k$ square tiles ($k^{2}$-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then, the system is diluted by removing $k^{2}$-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, $p_{c,k}$, for which the connectivity disappears. This particular value of the concentration is called textit{inverse percolation threshold}, and determines a well-defined geometrical phase transition in the system. The results obtained for $p_{c,k}$ show that the inverse percolation threshold is a decreasing function of $k$ in the range $1 leq k leq 4$. For $k geq 5$, all jammed configurations are percolating states, and consequently, there is no non-percolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent $ u_j$ was measured, being $ u_j = 1$ regardless of the size $k$ considered. In addition, the accurate determination of the critical exponents $ u$, $beta$ and $gamma$ reveals that the percolation phase transition involved in the system, which occurs for $k$ varying between 1 and 4, has the same universality class as the standard percolation problem.
In reconstituting k-mer models, extended objects which occupy several sites on a one dimensional lattice, undergo directed or undirected diffusion, and reconstitute -when in contact- by transferring a single monomer unit from one k-mer to the other; the rates depend on the size of participating k-mers. This polydispersed system has two conserved quantities, the number of k-mers and the packing fraction. We provide a matrix product method to write the steady state of this model and to calculate the spatial correlation functions analytically. We show that for a constant reconstitution rate, the spatial correlation exhibits damped oscillations in some density regions separated, from other regions with exponential decay, by a disorder surface. In a specific limit, this constant-rate reconstitution model is equivalent to a single dimer model and exhibits a phase coexistence similar to the one observed earlier in totally asymmetric simple exclusion process on a ring with a defect.
Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang $textit{et al.}$ [1] and Goremykina $textit{et al.}$ [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length $zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $tilde{zeta}$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $tilde{zeta}$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.
We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions which exhibits a mixed order transition (MOT), namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models which are seemingly unrelated. The model we present serves as a link between two classes of models which exhibit MOT in one dimension, namely, spin models with a coupling constant which decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.
We introduce an assisted exchange model (AEM) on a one dimensional periodic lattice with (K+1) different species of hard core particles, where the exchange rate depends on the pair of particles which undergo exchange and their immediate left neighbor. We show that this stochastic process has a pair factorized steady state for a broad class of exchange dynamics. We calculate exactly the particle current and spatial correlations (K+1)-species AEM using a transfer matrix formalism. Interestingly the current in AEM exhibits density dependent current reversal and negative differential mobility- both of which have been discussed elaborately by using a two species exchange model which resembles the partially asymmetric conserved lattice gas model in one dimension. Moreover, multi-species version of AEM exhibits additional features like multiple points of current reversal, and unusual response of particle current.
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