40,951 research outputs found

    Hard hexagon partition function for complex fugacity

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    We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

    Integrability vs non-integrability: Hard hexagons and hard squares compared

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    In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes 40×4040\times40 and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point z=−1z=-1 of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at z=−1z=-1 of the partition functions.Comment: 46 page

    Self-avoiding walks and polygons on the triangular lattice

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    We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, μ=4.150797226(26)\mu=4.150797226(26), and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure

    Statistics of lattice animals (polyominoes) and polygons

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    We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, τ=4.062570(8)\tau = 4.062570(8), for the growth constant of lattice animals and confirms to a very high degree of certainty that the generating function has a logarithmic divergence. We prove the bound τ>3.90318.\tau > 3.90318. We also calculate the radius of gyration of both lattice animals and polygons enumerated by area. The analysis of the radius of gyration series yields the estimate ν=0.64115(5)\nu = 0.64115(5), for both animals and polygons enumerated by area. The mean perimeter of polygons of area nn is also calculated. A number of new amplitude estimates are given.Comment: 10 pages, 2 eps figure

    Reaction-diffusion processes and non-perturbative renormalisation group

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    This paper is devoted to investigating non-equilibrium phase transitions to an absorbing state, which are generically encountered in reaction-diffusion processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev. Lett. 92, 255703; Phys. Rev. Lett. 95, 100601], of recent progress in this field that has been allowed by a non-perturbative renormalisation group approach. We mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non-perturbative features and that hence the use of a non-perturbative method turns out to be crucial to get a correct picture of the physics of these models.Comment: 14 pages, submitted to J. Phys. A for the proceedings of the conference 'Renormalization Group 2005', Helsink

    Effective temperature in driven vortex lattices with random pinning

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    We study numerically correlation and response functions in non-equilibrium driven vortex lattices with random pinning. From a generalized fluctuation-dissipation relation we calculate an effective transverse temperature in the fluid moving phase. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs. We also discuss how the effective temperature can be measured experimentally from a generalized Kubo formula.Comment: 4 pages, 4 figure

    Quantum Geometry and Diffusion

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    We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.Comment: latex2e, 10 pages, 4 figure

    A reduced model for shock and detonation waves. II. The reactive case

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    We present a mesoscopic model for reactive shock waves, which extends a previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A complex molecule (or a group of molecules) is replaced by a single mesoparticle, evolving according to some Dissipative Particle Dynamics. Chemical reactions can be handled in a mean way by considering an additional variable per particle describing a rate of reaction. The evolution of this rate is governed by the kinetics of a reversible exothermic reaction. Numerical results give profiles in qualitative agreement with all-atom studies

    Directed Percolation with long-range interactions: modeling non-equilibrium wetting

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    It is argued that some phase--transitions observed in models of non-equilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length ℓ\ell is 1+aℓ−σ1+a\ell^{-\sigma}. Mean--field analysis and numerical simulations indicate that for σ>1\sigma>1 the transition is continuous and belongs to the universality class of directed percolation, while for 0<σ<10<\sigma<1, the transition becomes first order. This criterion is then applied to discuss critical properties of various models of non--equilibrium wetting.Comment: 12 Figures. V Version resubmitted to Phys. Rev. E after referees repor
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