6,602 research outputs found
Some structural properties of two counter-examples to the Baker–Gammel–Wills conjecture
AbstractI improve the counter-example of Lubinsky, and show that the counter-example of Buslaev is also relevant to the original form of the Baker–Gammel–Wills conjecture. I notice that these counter-examples have only a single spurious pole and that a patchwork of just two subsequences of diagonal Padé approximants provides uniform convergence in compact subsets of |z|<1. I find that both counter-examples can be characterized by the observation that they are associated with bounded J-matrices. I prove a number of results for the convergence of diagonal Padé approximants to functions which have bounded J-matrices
Method for comparing finite temperature field theory results with lattice data
The values of the presently available truncated perturbative expressions for
the pressure of the quark-gluon plasma at finite temperatures and finite
chemical potential are trustworthy only at very large energies. When used down
to temperatures close to the critical one Tc, they suffer from large
uncertainties due to the renormalization scale freedom. In order to reduce
these uncertainties, we perform resummations of the pressure by applying
Pade-related approximants to the available perturbation series for the
short-distance and for the long-distance contributions. In the two
contributions, we use two different renormalization scales which reflect
different energy regions contributing to the different parts. Application of
the obtained expressions at low temperatures is made possible by replacing the
usual four-loop barMS beta function for alpha_s by its Borel-Pade resummation,
eliminating thus the unphysical Landau singularities of alpha_s. The obtained
results are remarkably insensitive to the chosen renormalization scale and can
be compared with lattice results -- for the pressure (p), the chemical
potential contribution (delta p) to the pressure, and various susceptibilities.
A good qualitative agreement with the lattice results is revealed down to
temperatures close to Tc.Comment: 24 pages, 17 figures, revtex4; Ref.[25] is new; the ordering of the
references and grammatic and stylistic errors are corrected - version as it
appears in PR
Scaling behavior at zero-temperature critical points
A scaling form for the logarithm of the partition function suitable for a zero-temperature critical point is obtained and found to hold for the spherical model in less than two dimensions and the classical n-component Heisenberg linear chain. Nevertheless, several cases are found where the critical-exponent relations involving the specific heat fail. These anomalous cases do not imply a breakdown of the scaling implicit in the basic formulation of renormalization-group theory
Improved Quantum Hard-Sphere Ground-State Equations of State
The London ground-state energy formula as a function of number density for a
system of identical boson hard spheres, corrected for the reduced mass of a
pair of particles in a sphere-of-influence picture, and generalized to fermion
hard-sphere systems with two and four intrinsic degrees of freedom, has a
double-pole at the ultimate \textit{regular} (or periodic, e.g.,
face-centered-cubic) close-packing density usually associated with a
crystalline branch. Improved fluid branches are contructed based upon exact,
field-theoretic perturbation-theory low-density expansions for many-boson and
many-fermion systems, appropriately extrapolated to intermediate densities, but
whose ultimate density is irregular or \textit{random} closest close-packing as
suggested in studies of a classical system of hard spheres. Results show
substantially improved agreement with the best available Green-function Monte
Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder,
variational Fermi hypernetted chain, and so-called L-expansion data for
two-component fermions.Comment: 15 pages and 7 figure
Bose-Einstein Condensation in the Relativistic Ideal Bose Gas
The Bose-Einstein condensation (BEC) critical temperature in a relativistic
ideal Bose gas of identical bosons, with and without the antibosons expected to
be pair-produced abundantly at sufficiently hot temperatures, is exactly
calculated for all boson number-densities, all boson point rest masses, and all
temperatures. The Helmholtz free energy at the critical BEC temperature is
found to be lower, thus implying that the omission of antibosons always leads
to the computation of a metastable state.Comment: 10 pages, 4 figure
Critical indices from perturbation analysis of the Callan-Symanzik equation
Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained
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