11,856 research outputs found
Functional renormalization group approach to the Yang-Lee edge singularity
We determine the scaling properties of the Yang-Lee edge singularity as
described by a one-component scalar field theory with imaginary cubic coupling,
using the nonperturbative functional renormalization group in
Euclidean dimensions. We find very good agreement with high-temperature series
data in dimensions and compare our results to recent estimates of
critical exponents obtained with the four-loop expansion and
the conformal bootstrap. The relevance of operator insertions at the
corresponding fixed point of the RG functions is discussed and we
estimate the error associated with truncations of the
scale-dependent effective action.Comment: 10 pages, 4 figures, updated reference to supplementary materia
On spinodal points and Lee-Yang edge singularities
We address a number of outstanding questions associated with the analytic
properties of the universal equation of state of the theory, which
describes the critical behavior of the Ising model and ubiquitous critical
points of the liquid-gas type. We focus on the relation between spinodal points
that limit the domain of metastability for temperatures below the critical
temperature, i.e., , and Lee-Yang edge singularities that
restrict the domain of analyticity around the point of zero magnetic field
for . The extended analyticity conjecture (due to Fonseca and
Zamolodchikov) posits that, for , the Lee-Yang edge
singularities are the closest singularities to the real axis. This has
interesting implications, in particular, that the spinodal singularities must
lie off the real axis for , in contrast to the commonly known result
of the mean-field approximation. We find that the parametric representation of
the Ising equation of state obtained in the expansion, as
well as the equation of state of the -symmetric theory at
large , are both nontrivially consistent with the conjecture. We analyze the
reason for the difficulty of addressing this issue using the
expansion. It is related to the long-standing paradox associated with the fact
that the vicinity of the Lee-Yang edge singularity is described by Fisher's
theory, which remains nonperturbative even for , where the
equation of state of the theory is expected to approach the mean-field
result. We resolve this paradox by deriving the Ginzburg criterion that
determines the size of the region around the Lee-Yang edge singularity where
mean-field theory no longer applies.Comment: 26 pages, 8 figures; v2: shortened Sec. 4.1 and streamlined
arguments/notation in Sec. 4.2, details moved to appendix, added reference 1
Race and Socioeconomic Factors Affect Opportunities for Better Health
Examines racial/ethnic disparities in mortality and diabetes rates and the links between income and health within and across groups. Explores how race/ethnicity affects income at a given education level or socioeconomic conditions at a given income level
Variable Hardy Spaces
We develop the theory of variable exponent Hardy spaces. Analogous to the
classical theory, we give equivalent definitions in terms of maximal operators.
We also show that distributions in these spaces have an atomic decomposition
including a "finite" decomposition; this decomposition is more like the
decomposition for weighted Hardy spaces due to Stromberg and Torchinsky than
the classical atomic decomposition. As an application of the atomic
decomposition we show that singular integral operators are bounded on variable
Hardy spaces with minimal regularity assumptions on the exponent function
Improving Christofides' Algorithm for the s-t Path TSP
We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t
path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices
including two prespecified endpoints, the problem is to find a shortest
Hamiltonian path between the two endpoints; Hoogeveen showed that the natural
variant of Christofides' algorithm is a 5/3-approximation algorithm for this
problem, and this asymptotically tight bound in fact has been the best
approximation ratio known until now. We modify this algorithm so that it
chooses the initial spanning tree based on an optimal solution to the Held-Karp
relaxation rather than a minimum spanning tree; we prove this simple but
crucial modification leads to an improved approximation ratio, surpassing the
20-year-old barrier set by the natural Christofides' algorithm variant. Our
algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of
the path-variant Held-Karp relaxation. The techniques devised in this paper can
be applied to other optimization problems as well: these applications include
improved approximation algorithms and improved LP integrality gap upper bounds
for the prize-collecting s-t path problem and the unit-weight graphical metric
s-t path TSP.Comment: 31 pages, 5 figure
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