688 research outputs found
A constrained Potts antiferromagnet model with an interface representation
We define a four-state Potts model ensemble on the square lattice, with the
constraints that neighboring spins must have different values, and that no
plaquette may contain all four states. The spin configurations may be mapped
into those of a 2-dimensional interface in a 2+5 dimensional space. If this
interface is in a Gaussian rough phase (as is the case for most other models
with such a mapping), then the spin correlations are critical and their
exponents can be related to the stiffness governing the interface fluctuations.
Results of our Monte Carlo simulations show height fluctuations with an
anomalous dependence on wavevector, intermediate between the behaviors expected
in a rough phase and in a smooth phase; we argue that the smooth phase (which
would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.
Invaded cluster algorithm for a tricritical point in a diluted Potts model
The invaded cluster approach is extended to 2D Potts model with annealed
vacancies by using the random-cluster representation. Geometrical arguments are
used to propose the algorithm which converges to the tricritical point in the
two-dimensional parameter space spanned by temperature and the chemical
potential of vacancies. The tricritical point is identified as a simultaneous
onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of
"geometrical disorder cluster". The location of the tricritical point and the
concentration of vacancies for q = 1, 2, 3 are found to be in good agreement
with the best known results. Scaling properties of the percolating scaling
cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure
Biot-Savart correlations in layered superconductors
We discuss the superconductor to normal phase transition in an
infinite-layered type-II superconductor in the limit where the Josephson
coupling between layers is negligible. We model each layer as a neutral gas of
thermally excited pancake vortices. We assume the dominant interaction between
vortices in the same and in different layers is the electromagnetic interaction
between the screening currents induced by these vortices. Our main result,
obtained by exactly solving the leading order renormalization group flow, is
that the phase transition in this model is a Kosterlitz--Thouless transition
despite being a three--dimensional system. While the transition itself is
driven by the unbinding of two-dimensional pancake vortices, an RG analysis of
the low temperature phase and a mean-field theory of the high temperature phase
reveal that both phases possess three-dimensional correlations. An experimental
consequence of this is that the jump in the measured in-plane superfluid
stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will
receive a small non--universal correction (of order 1% in
BiSrCaCuO). This overall picture places some claims
expressed in the literature on a more secure analytical footing and also
resolves some conflicting views.Comment: 16 pages, 2 figures; minor typos corrected, references adde
An exact universal amplitude ratio for percolation
The universal amplitude ratio for percolation in two
dimensions is determined exactly using results for the dilute A model in regime
1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to
correct error
Rotationally induced vortices in optical cavity modes
We show that vortices appear in the modes of an astigmatic optical cavity
when it is put into rotation about its optical axis. We study the properties of
these vortices and discuss numerical results for a specific realization of such
a set-up. Our method is exact up to first order in the time-dependent paraxial
approximation and involves bosonic ladder operators in the spirit of the
quantum-mechanical harmonic oscillator.Comment: 8 pages, 5 figures. Accepted for publication in a special issue
(singular optics 2008) of Journal of Optics A: Pure and Applied Optic
Into the depths of C: Elaborating the de facto standards
C remains central to our computing infrastructure. It is notionally defined by ISO standards, but in reality the properties of C assumed by systems code and those implemented by compilers have diverged, both from the ISO standards and from each other, and none of these are clearly understood. We make two contributions to help improve this error-prone situation. First, we describe an in-depth analysis of the design space for the semantics of pointers and memory in C as it is used in practice. We articulate many specific questions, build a suite of semantic test cases, gather experimental data from multiple implementations, and survey what C experts believe about the de facto standards. We identify questions where there is a consensus (either following ISO or differing) and where there are conflicts. We apply all this to an experimental C implemented above capability hardware. Second, we describe a formal model, Cerberus, for large parts of C. Cerberus is parameterised on its memory model; it is linkable either with a candidate de facto memory object model, under construction, or with an operational C11 concurrency model; it is defined by elaboration to a much simpler Core language for accessibility, and it is executable as a test oracle on small examples. This should provide a solid basis for discussion of what mainstream C is now: what programmers and analysis tools can assume and what compilers aim to implement. Ultimately we hope it will be a step towards clear, consistent, and accepted semantics for the various use-cases of C.We acknowledge funding from EPSRC grants EP/H005633 (Leadership Fellowship, Sewell) and EP/K008528 (REMS Programme Grant), and a Gates Cambridge Scholarship (Nienhuis). This work is also part of the CTSRD projects sponsored by the Defense Advanced Research Projects Agency (DARPA) and the Air Force Research Laboratory (AFRL), under contract FA8750-10-C-0237.This is the author accepted manuscript. The final version is available from the Association for Computing Machinery via http://dx.doi.org/10.1145/2908080.290808
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An Operational Semantics for C/C++11 Concurrency
The C/C++11 concurrency model balances two goals: it is relaxed enough to be efficiently implementable and (leaving aside the "thin-air" problem) it is strong enough to give useful guarantees to programmers. It is mathematically precise and has been used in verification research and compiler testing. However, the model is expressed in an axiomatic style, as predicates on complete candidate executions. This suffices for computing the set of allowed executions of a small litmus test, but it does not directly support the incremental construction of executions of larger programs. It is also at odds with conventional operational semantics, as used implicitly in the rest of the C/C++ standards. Our main contribution is the development of an operational model for C/C++11 concurrency. This covers all the features of the previous formalised axiomatic model, and we have a mechanised proof that the two are equivalent, in Isabelle/ HOL. We also integrate this semantics with an operational semantics for sequential C (described elsewhere); the combined semantics can incrementally execute programs in a small fragment of C. Doing this uncovered several new aspects of the C/C++11 model: we show that one cannot build an equivalent operational model that simply follows program order, sequential consistent order, or the synchronises-with order. The first negative result is forced by hardware-observable behaviour, but the latter two are not, and so might be ameliorated by changing C/C++11. More generally, we hope that this work, with its focus on incremental construction of executions, will inform the future design of new concurrency models.This work was partly funded by a Gates studentship (Nienhuis) and by the EPSRC Programme Grant REMS: Rigorous Engineering for Mainstream Systems, EP/K008528/1
All-optical 3D atomic loops generated with Bessel light fields
The propagation invariance of Bessel beams as well as their transversal
structure are used to perform a comparative analysis of their effect on cold
atoms for four different configurations and combinations thereof. We show that,
even at temperatures for which the classical description of the atom center of
mass motion is valid, the interchange of momentum, energy and orbital angular
momentum between light and atoms yields efficient tools for all-optical
trapping, transporting and, in general, manipulating the state of motion of
cold atoms.Comment: 13 pages, 9 figure
A Simple Model of Liquid-liquid Phase Transitions
In recent years, a second fluid-fluid phase transition has been reported in
several materials at pressures far above the usual liquid-gas phase transition.
In this paper, we introduce a new model of this behavior based on the
Lennard-Jones interaction with a modification to mimic the different kinds of
short-range orientational order in complex materials. We have done Monte Carlo
studies of this model that clearly demonstrate the existence of a second
first-order fluid-fluid phase transition between high- and low-density liquid
phases
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