Hierarchic trees with branching number close to one: noiseless KPZ equation with additional linear term for imitation of 2-d and 3-d phase transitions.

An imitation of 2d field theory is formulated by means of a model on the hierarhic tree (with branching number close to one) with the same potential and the free correlators identical to 2d correlators ones. Such a model carries on some features of the original model for certain scale invariant theories. For the case of 2d conformal models it is possible to derive exact results. The renormalization group equation for the free energy is noiseless KPZ equation with additional linear term.Comment: latex, 5 page

Two-way traffic flow: exactly solvable model of traffic jam

We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other one. When the interchannel interaction reaches a critical value, traffic jam occurs, which turns out to be of first order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the $k$- point density correlation functions. We also obtain the exact probability of two cars in one lane being distance $R$ apart, provided there is a finite density of cars on the other lane, and show the two cars form a weakly bound state in the jammed phase.Comment: 17 pages, Latex, ioplppt.sty, 11 ps figure

Large Deviation Function of the Partially Asymmetric Exclusion Process

The large deviation function obtained recently by Derrida and Lebowitz for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.Comment: 10 pages, 2 eps figures, minor changes, submitted to PR

Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199

Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions

The non-equilibrium dynamics of the strongly diluted random-bond Ising model in two-dimensions (2d) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a non-zero, dilution-dependent, value $P(\infty)$. We find that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-dilution considered. Our findings, which are consistent with a recent result of Newman and Stein, suggest that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the dilution present.Comment: some minor changes to the text, one additional referenc

Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

The political import of deconstruction—Derrida’s limits?: a forum on Jacques Derrida’s specters of Marx after 25 Years, part I

Jacques Derrida delivered the basis of The Specters of Marx: The State of the Debt, the Work of Mourning, & the New International as a plenary address at the conference ‘Whither Marxism?’ hosted by the University of California, Riverside, in 1993. The longer book version was published in French the same year and appeared in English and Portuguese the following year. In the decade after the publication of Specters, Derrida’s analyses provoked a large critical literature and invited both consternation and celebration by figures such as Antonio Negri, Wendy Brown and Frederic Jameson. This forum seeks to stimulate new reflections on Derrida, deconstruction and Specters of Marx by considering how the futures past announced by the book have fared after an eventful quarter century. Maja Zehfuss, Antonio Vázquez-Arroyo and Dan Bulley and Bal Sokhi-Bulley offer sharp, occasionally exasperated, meditations on the political import of deconstruction and the limits of Derrida’s diagnoses in Specters of Marx but also identify possible paths forward for a global politics taking inspiration in Derrida’s work of the 1990s

Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics

Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our recent exact results for a finite chain with open boundaries. The corresponding results for sublattice parallel dynamics follow from the relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)] and for parallel dynamics from the mapping found by Evans, Rajewsky and Speer [J. Stat. Phys. 95, 45 (1999)]. By comparing the asymptotic results appropriate for parallel update with those published in the latter paper, we correct some technical errors in the final results given there.Comment: About 10 pages and 3 figures, new references are added and a comparison is made with the results by de Gier and Nienhuis [Phys. Rev. E 59, 4899(1999)

On the genealogy of a population of biparental individuals

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.Comment: 14 pages, 7 figures, to appear in the Journal of Theoretical Biolog