Real-space renormalisation group approach to driven diffusive systems

We introduce a real-space renormalisation group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.Comment: 10 pages, 5 figure

Quantum Scaling Approach to Nonequilibrium Models

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality symmetries, yielding exact fixed points for a variety of exclusion models. In addition, it is shown how the asymmetric simple exclusion process in one dimension can be written in terms of a classical Hamiltonian in two dimensions using a Suzuki-Trotter decomposition.Comment: 17 page

Spatially heterogeneous dynamics in granular compaction

We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.Comment: 4 pages, 3 figure

Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure

Randomly Diluted e_g Orbital-Ordered Systems

Dilution effects on the long-range ordered state of the doubly degenerate $e_g$ orbital are investigated. Quenched impurities without the orbital degree of freedom are introduced in the orbital model where the long-range order is realized by the order-from-disorder mechanism. It is shown by the Monte-Carlo simulation and the cluster-expansion method that a decrease in the orbital ordering temperature by dilution is remarkable in comparison with that in the randomly diluted spin models. Tiltings of orbitals around impurity cause this unique dilution effects on the orbital systems. The present theory provides a new view point for the recent experiments in KCu$_{1-x}$Zn$_x$F$_3$.Comment: 4 pages, 4 figure

Duality and phase diagram of one dimensional transport

The observation of duality by Mukherji and Mishra in one dimensional transport problems has been used to develop a general approach to classify and characterize the steady state phase diagrams. The phase diagrams are determined by the zeros of a set of coarse-grained functions without the need of detailed knowledge of microscopic dynamics. In the process, a new class of nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files

Exact probability function for bulk density and current in the asymmetric exclusion process

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques, and by introducing a modified version of the original operator algebra. As a byproduct of these considerations we also arrive at a novel and very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure

Disordered two-dimensional superconductors: roles of temperature and interaction strength

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction $f$ of sites, while keeping a finite $U$ on the remaining ones. Through Quantum Monte Carlo (QMC) simulations for several values of $f$ and $U$, and for system sizes ranging from $8\times 8$ to $16\times 16$, we have calculated the configurational averages of the equal-time pair structure factor $P_s$, and, for a more restricted set of variables, the helicity modulus, $\rho_s$, as functions of temperature. Two finite-size scaling {\it ansatze} for $P_s$ have been used, one for zero-temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration, $f_c$, which increases with $U$, at least up to U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of $f$ shows a maximum near $f\sim 0.07$, for $2\lesssim U\lesssim 6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of $f$, for $U=3,$ 4 and 6: they also show maxima near $f\sim 0.07$, with the highest $T_c$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of CDW-superconductivity degeneracy and the fact that free sites tend to "push" electrons towards attractive sites, the latter effect being more drastic at weak couplings.Comment: 9 two-column pages, 14 figures, RevTe

Domain scaling and marginality breaking in the random field Ising model

A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A h^{-\gamma}\right)$ in $d=2$, and for $d=2+\epsilon$ power law behaviour with $\nu = 2/\epsilon \gamma$, $h^\star \sim \epsilon^{1/\gamma}$. Here, $\gamma = 2,4/3$ (lattice, continuum) is one of four rough wall exponents provided by the theory. The analysis is substantiated by three different numerical techniques (transfer matrix, Monte Carlo, ground state algorithm). These provide for strips up to width $L=11$ basic ingredients of the theory, namely free energy, domain size, and roughening data and exponents.Comment: ReVTeX v3.0, 19 pages plus 19 figures uuencoded in a separate file. These are self-unpacking via a shell scrip

A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability $\alpha$ that a particle will flow into the chain to the leftmost site, the probability $\beta$ that a particle will flow out from the rightmost site, and the probability $p$ that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.Comment: 14 pages, 4 figure