67,152 research outputs found
Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
We analyze the scaling and finite-size-scaling behavior of the
two-dimensional 4-state Potts model. We find new multiplicative logarithmic
corrections for the susceptibility, in addition to the already known ones for
the specific heat. We also find additive logarithmic corrections to scaling,
some of which are universal. We have checked the theoretical predictions at
criticality and off criticality by means of high-precision Monte Carlo data.Comment: 46 pages including 8 figures. Self-unpacking file containing the tex
file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 8 ps file
Cluster algorithm for non-additive hard-core mixtures
In this paper, we present a cluster algorithm for the numerical simulations
of non-additive hard-core mixtures. This algorithm allows one to simulate and
equilibrate systems with a number of particles two orders of magnitude larger
than previous simulations. The phase separation for symmetric binary mixtures
is studied for different non-additvities as well as for the Widom-Rowlinson
model (B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)) in two and
three dimensions. The critical densities are determined from finite size
scaling. The critical exponents for all the non-additivities are consistent
with the Ising universality class.Comment: 11 pages and 9 figures, to be published in J. Chem. Phys. Minor
corrections and some references adde
Adiabatic quantum algorithm for search engine ranking
We propose an adiabatic quantum algorithm for generating a quantum pure state
encoding of the PageRank vector, the most widely used tool in ranking the
relative importance of internet pages. We present extensive numerical
simulations which provide evidence that this algorithm can prepare the quantum
PageRank state in a time which, on average, scales polylogarithmically in the
number of webpages. We argue that the main topological feature of the
underlying web graph allowing for such a scaling is the out-degree
distribution. The top ranked entries of the quantum PageRank state
can then be estimated with a polynomial quantum speedup. Moreover, the quantum
PageRank state can be used in "q-sampling" protocols for testing properties of
distributions, which require exponentially fewer measurements than all
classical schemes designed for the same task. This can be used to decide
whether to run a classical update of the PageRank.Comment: 7 pages, 5 figures; closer to published versio
Improved Distributed Algorithms for Exact Shortest Paths
Computing shortest paths is one of the central problems in the theory of
distributed computing. For the last few years, substantial progress has been
made on the approximate single source shortest paths problem, culminating in an
algorithm of Becker et al. [DISC'17] which deterministically computes
-approximate shortest paths in time, where
is the hop-diameter of the graph. Up to logarithmic factors, this time
complexity is optimal, matching the lower bound of Elkin [STOC'04].
The question of exact shortest paths however saw no algorithmic progress for
decades, until the recent breakthrough of Elkin [STOC'17], which established a
sublinear-time algorithm for exact single source shortest paths on undirected
graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for
exact all pairs shortest paths problem on directed graphs.
In this paper, we present a new single-source shortest path algorithm with
complexity . For polylogarithmic , this improves
on Elkin's bound and gets closer to the
lower bound of Elkin [STOC'04]. For larger values of
, we present an improved variant of our algorithm which achieves complexity
, and
thus compares favorably with Elkin's bound of in essentially the entire range of parameters. This
algorithm provides also a qualitative improvement, because it works for the
more challenging case of directed graphs (i.e., graphs where the two directions
of an edge can have different weights), constituting the first sublinear-time
algorithm for directed graphs. Our algorithm also extends to the case of exact
-source shortest paths...Comment: 26 page
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