37,504 research outputs found

    Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte

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    Grand canonical simulations at various levels, ζ=5\zeta=5-20, of fine- lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or RPM. With the aid of finite-size scaling analyses it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of ζ\zeta (\grtsim 4); thus the continuum (ζ→∞)(\zeta\to\infty) RPM exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the {\em intrinsically} erratic ζ\zeta-dependence, yielding (\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the ζ=∞\zeta=\infty RPM.Comment: 4 pages including 4 figure

    Lebesgue-type inequalities in sparse sampling recovery

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    Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type algorithm -- Weak Orthogonal Matching Pursuit -- based on good points for universal discretization provides effective recovery in the square norm. In this paper we extend those results by replacing the square norm with other integral norms. In this case we need to conduct our analysis in a Banach space rather than in a Hilbert space, making the techniques more involved. In particular, we establish that a greedy type algorithm -- Weak Chebyshev Greedy Algorithm -- based on good points for the LpL_p-universal discretization provides good recovery in the LpL_p norm for 2≤p<∞2\le p<\infty. Furthermore, we discuss the problem of stable recovery and demonstrate its close relationship with sampling discretization

    On universal sampling recovery in the uniform norm

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    It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol'skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions on two variables, where the Fibonacci point sets are used for recovery.Comment: arXiv admin note: text overlap with arXiv:2201.0041

    First-order phase transition of the tethered membrane model on spherical surfaces

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    We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of Nambu and Goto. These are curvature models for biological membranes including artificial vesicles. The results obtained in this paper indicate that the first-order phase transition is universal in the sense that the order of the transition is independent of discretization of the Hamiltonian for the tethered surface model.Comment: 22 pages with 14 figure

    Transitions and crossover phenomena in fully frustrated XY systems

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    We study the two-dimensional fully frustrated XY (FFXY) model and two related models, a discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model and a coupled Ising-XY model, by means of Monte Carlo simulations on square lattices L x L, L=O(10^3). We show that their phase diagram is characterized by two very close chiral and spin transitions, at T_ch > T_sp respectively, of the Ising and Kosterlitz-Thouless type. At T_ch the Ising regime sets in only after a preasymptotic regime, which appears universal to some extent. The approach is nonmonotonic for most observables, with a wide region controlled by an effective exponent nu_eff=0.8.Comment: 9 page
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