37,504 research outputs found
Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte
Grand canonical simulations at various levels, -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 (\grtsim 4); thus the continuum 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 -dependence, yielding
(\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the
RPM.Comment: 4 pages including 4 figure
Lebesgue-type inequalities in sparse sampling recovery
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 -universal discretization provides good
recovery in the norm for . Furthermore, we discuss the
problem of stable recovery and demonstrate its close relationship with sampling
discretization
On universal sampling recovery in the uniform norm
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
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
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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