8,587 research outputs found

    Pressure of Membrane between Walls

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    For a single membrane of stiffness kappa fluctuating between two planar walls of distance d, we calculate analytically the proportionality constant in the pressure law p proportional to T^2/kappa^2 d^3, in very good agreement with results from Monte Carlo simulations.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re277/preprint.htm

    Multigrid Method versus Staging Algorithm for PIMC Simulations

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    We present a comparison of the performance of two non-local update algorithms for path integral Monte Carlo (PIMC) simulations, the multigrid Monte Carlo method and the staging algorithm. Looking at autocorrelation times for the internal energy we show that both refined algorithms beat the slowing down which is encountered for standard local update schemes in the continuum limit. We investigate the conditions under which the staging algorithm performs optimally and give a brief discussion of the mutual merits of the two algorithms.Comment: 11 pp. LaTeX, 4 Postscript Figure

    Critical Exponents from General Distributions of Zeroes

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    All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using finite-size data of the type typically garnered from a computational approach. Here that method is extended to deal with more general cases. Other critical points of a type which appear in many models are also studied.Comment: 4 pages, 3 figure

    Correlation Length From Cluster-Diameter Distribution

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    We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the disordered phase at the transition point for q=10q=10, 15, and 20 with an accuracy of about 11%-2%. This is a considerable improvement over previous measurements using the standard (projected) two-point function.Comment: 4 pages, PostScript, contribution to LATTICE95. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

    New methods to measure phase transition strength

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    A recently developed technique to determine the order and strength of phase transitions by extracting the density of partition function zeroes (a continuous function) from finite-size systems (a discrete data set) is generalized to systems for which (i) some or all of the zeroes occur in degenerate sets and/or (ii) they are not confined to a singular line in the complex plane. The technique is demonstrated by application to the case of free Wilson fermions.Comment: 3 pages, 2 figures, Lattice2002(spin

    Information Geometry and Phase Transitions

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    The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur

    Parallel-tempering cluster algorithm for computer simulations of critical phenomena

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    In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.Comment: pages, 5 figures, and 2 table

    Phase Transition Strength through Densities of General Distributions of Zeroes

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    A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane and/or come in degenerate sets. The efficacy of the approach is demonstrated by application to a number of models for which these features are manifest and the zeroes are readily calculable.Comment: 16 pages, 12 figure

    Multibondic Cluster Algorithm

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    Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for qq-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with q=7,10q=7, 10 and 2020 show that the autocorrelation times of this algorithm grow with the system size VV as τVα\tau \propto V^\alpha, where the exponent takes the optimal random walk value of α1\alpha \approx 1.Comment: 3 pages, uuencoded compressed postscript file, contribution to the LATTICE'94 conferenc

    The Wrong Kind of Gravity

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    The KPZ formula shows that coupling central charge less than one spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on the central charge. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins. Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the ``wrong'' central charge. We might then expect to see the critical exponents appropriate to the central charge used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the Ising, tricritical Ising and 3-state Potts models.Comment: 8 pages, no figure
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