1,679 research outputs found

    2D Potts Model Correlation Lengths: Numerical Evidence for ξo=ξd\xi_o = \xi_d at βt\beta_t

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    We have studied spin-spin correlation functions in the ordered phase of the two-dimensional qq-state Potts model with q=10q=10, 15, and 20 at the first-order transition point βt\beta_t. Through extensive Monte Carlo simulations we obtain strong numerical evidence that the correlation length in the ordered phase agrees with the exactly known and recently numerically confirmed correlation length in the disordered phase: ξo(βt)=ξd(βt)\xi_o(\beta_t) = \xi_d(\beta_t). As a byproduct we find the energy moments in the ordered phase at βt\beta_t in very good agreement with a recent large qq-expansion.Comment: 11 pages, PostScript. To appear in Europhys. Lett. (September 1995). See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

    Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

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    We report numerical simulations of two-dimensional qq-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function Gdiam(x)G_{diam}(x), which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter xx, Gdiamexp(x/ξ)G_{diam} \propto \exp(-x/\xi), where ξ\xi is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with q=10q=10, 15, and 2020 on large square lattices of size 300×300300 \times 300, 120×120120 \times 120, and 80×8080 \times 80, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length ξd(βt)\xi_d(\beta_t) in the disordered phase at the first-order transition point βt\beta_t with an accuracy of about 11%-2% for all considered values of qq. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

    Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ϕ4\phi^4-Model: Autocorrelations and Interface Tension

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    We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar ϕ4\phi^4-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as uuencoded compressed tar fil

    Percolation of Vortices in the 3D Abelian Lattice Higgs Model

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    The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is investigated by means of percolation observables. In the region of the phase diagram where the Higgs and confinement phases are separated by a first-order transition, it is shown that the vortices percolate right at the phase boundary, and that the first-order nature of the transition is reflected by the network. In the crossover region, where the phase boundary ceases to be first order, the vortices are shown to still percolate. In contrast to other observables, the percolation observables show finite-size scaling. The exponents characterizing the critical behavior of the vortices in this region are shown to fall in the random percolation universality class.Comment: 24 pages, 12 figure

    Thickness-dependent secondary structure formation of tubelike polymers

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    By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global radius of curvature of a polymer conformation, accounts for the excluded volume of the polymer and induces cooperative effects supporting the formation of secondary structures. In our detailed analysis of the temperature and thickness dependence of the conformational behavior for classes of short tubelike polymers, we find that known secondary-structure segments like helices and turns, but also ringlike conformations and stiff rods are dominant intrinsic topologies governing the phase behavior of such cooperative tubelike objects. This shows that the thickness constraint is indeed a fundamental physical parameter that allows for a classification of generic polymer structures

    Two Anderson impurities in a 2D host with Rashba spin-orbit interaction

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    We have studied the two-dimensional two-impurity Anderson model with additional Rashba spin-orbit interaction by means of the modified perturbation theory. The impurity Green's functions we have constructed exactly reproduce the first four spectral moments. We discuss the height and the width of the even/odd Kondo peaks as functions of the inter-impurity distance and the Rashba energy ERE_R (the strength of the Rashba spin-orbit interaction). For small impurity separations the Kondo temperature shows a non-monotonic dependence on ERE_R being different in the even and the odd channel. We predict that the Kondo temperature has only almost linear dependence on ERE_R and not an exponential increase with ERE_RComment: To be published in Phys. Rev.

    The Interface Tension in Quenched QCD at the Critical Temperature

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    We present results for the confinement-deconfinement interface tension αcd\alpha_{cd} of quenched QCD. They were obtained by applying Binder's histogram method to lattices of size L2×Lz×LtL^2\times L_z\times L_t for Lt=2L_t=2 and L=8,10,12\mbox{ and }14 with Lz=30L_z=30 for L=8L=8 and Lz=3LL_z=3L otherwise. The use of a multicanonical algorithm and cylindrical geometries have turned out to be crucial for the numerical studies.Comment: (talk presented by B. Grossmann at Lattice 92), 4 pages with 5 figure appended as encapsulated postscript files at the end, preprint HLRZ-92-7

    Monopole action from vacuum configurations in compact QED

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    It is possible to derive a monopole action from vacuum configurations obtained in Monte-Carlo simulations extending the method developed by Swendsen. We apply the method to compact QED both in the Villain and in the Wilson forms. The action of the natural monopoles in the Villain case is in fairly good agreement with that derived by the exact dual transformation. Comparing the monopole actions, we find (1) the DeGrand-Toussaint monopole definition may be useful for βV\beta_V larger than about 0.5, (2) the Villain model well approximates the Wilson one for β\beta smaller than βc\beta_c and (3) in the Wilson action the monopole condensation occurs in the confinement phase and βc\beta_c may be explained by the energy-entropy balance of monopole loops like in the Villain case.Comment: 12 Pages+7 figures, KANAZAWA 94-1
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