701 research outputs found
General duality for abelian-group-valued statistical-mechanics models
We introduce a general class of statistical-mechanics models, taking values
in an abelian group, which includes examples of both spin and gauge models,
both ordered and disordered. The model is described by a set of ``variables''
and a set of ``interactions''. A Gibbs factor is associated to each variable
and to each interaction. We introduce a duality transformation for systems in
this class. The duality exchanges the abelian group with its dual, the Gibbs
factors with their Fourier transforms, and the interactions with the variables.
High (low) couplings in the interaction terms are mapped into low (high)
couplings in the one-body terms. The idea is that our class of systems extends
the one for which the classical procedure 'a la Kramers and Wannier holds, up
to include randomness into the pattern of interaction. We introduce and study
some physical examples: a random Gaussian Model, a random Potts-like model, and
a random variant of discrete scalar QED. We shortly describe the consequence of
duality for each example.Comment: 26 pages, 2 Postscript figure
Grassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J.
Phys.
The 1561 Earthquake(s) in Southern Italy: New Insights into a Complex Seismic Sequence
In the summer of 1561, a strong seismic sequence struck southern Italy, then the Spanish-ruled
Kingdom of Naples. Both the Italian seismological tradition and the latest catalogues locate it in
the Vallo di Diano (Diano Valley), a low-seismicity intermontane basin 100 km south-east of
Naples. We explore the hypothesis that current perception of the 1561 earthquake is distorted by
the nature of the historical dataset from which its parameters have been assessed, and which mostly
derive from a single—albeit very detailed—primary source. We present and discuss several previously
unconsidered original accounts. Our results cast doubts on the traditional interpretation of
the earthquake, which could have been either one Vallo di Diano mainshock or several strong
earthquakes within a time/space window compact enough for contemporary viewers to perceive
them as one. Unquestionably, there is much more to the 1561 earthquake(s) than previously
appeared. We hope that this groundbreaking effort will rekindle the interest of the seismological
community in this seismic episode, our knowledge of which is still far from complete
A General Limitation on Monte Carlo Algorithms of Metropolis Type
We prove that for any Monte Carlo algorithm of Metropolis type, the
autocorrelation time of a suitable ``energy''-like observable is bounded below
by a multiple of the corresponding ``specific heat''. This bound does not
depend on whether the proposed moves are local or non-local; it depends only on
the distance between the desired probability distribution and the
probability distribution for which the proposal matrix satisfies
detailed balance. We show, with several examples, that this result is
particularly powerful when applied to non-local algorithms.Comment: 8 pages, LaTeX plus subeqnarray.sty (included at end),
NYU-TH-93/07/01, IFUP-TH33/9
Random Walks with Long-Range Self-Repulsion on Proper Time
We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included)
IFUP-Th 13/92 and SNS 14/9
Dynamic Critical Behavior of an Extended Reptation Dynamics for Self-Avoiding Walks
We consider lattice self-avoiding walks and discuss the dynamic critical
behavior of two dynamics that use local and bilocal moves and generalize the
usual reptation dynamics. We determine the integrated and exponential
autocorrelation times for several observables, perform a dynamic finite-size
scaling study of the autocorrelation functions, and compute the associated
dynamic critical exponents . For the variables that describe the size of the
walks, in the absence of interactions we find in two dimensions
and in three dimensions. At the -point in two dimensions
we have .Comment: laTeX2e, 32 pages, 11 eps figure
O(N) and RP^{N-1} Models in Two Dimensions
I provide evidence that the 2D model for is equivalent
to the -invariant non-linear -model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint and models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling are
presented. The data confirm that the constraint model is in the samei
universality class as the model with standard action. I show that the
differences in the finite size scaling curves of i and models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that and models
share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode
When is a Partner not a Partner? Conceptualisations of 'family' in EU Free Movement Law
This paper considers the definitions of spouse, civil partner and partner in European Union (EU) free movement of persons law in order to question the EU's heterocentric approach to defining 'family' in this context. It argues that the term 'spouse' should include same-sex married partners in order to ensure that there is no discrimination on the grounds of sexual orientation. It further highlights the problems created by basing free movement rights of civil partners on host state recognition of such partnerships. This approach allows Member States to discriminate on the grounds of sexual orientation and is therefore not compatible with EU equality law in others areas. The position of unmarried or unregistered partners is also considered; in particular, the paper examines the requirement of a duly-attested durable relationship and its impact on same-sex partners wishing to move from one Member State to another. The paper argues that it is time to reconsider the law in this area and bring it in line with the EU's commitment to eliminate discrimination on several grounds, including sexual orientation. © 2011 Taylor and Francis Group, LLC
The Critical Hopping Parameter in O(a) improved Lattice QCD
We calculate the critical value of the hopping parameter, , in O(a)
improved Lattice QCD, to two loops in perturbation theory. We employ the
Sheikholeslami-Wohlert (clover) improved action for Wilson fermions.
The quantity which we study is a typical case of a vacuum expectation value
resulting in an additive renormalization; as such, it is characterized by a
power (linear) divergence in the lattice spacing, and its calculation lies at
the limits of applicability of perturbation theory.
The dependence of our results on the number of colors , the number of
fermionic flavors , and the clover parameter , is shown
explicitly. We compare our results to non perturbative evaluations of
coming from Monte Carlo simulations.Comment: 11 pages, 2 EPS figures. The only change with respect to the original
version is inclusion of the standard formulae for the gauge fixing and ghost
parts of the action. Accepted for publication in Physical Review
Nonequilibrium Reweighting on the Driven Diffusive Lattice Gas
The nonequilibrium reweighting technique, which was recently developed by the
present authors, is used for the study of the nonequilibrium steady states. The
renewed formulation of the nonequlibrium reweighting enables us to use the very
efficient multi-spin coding. We apply the nonequilibrium reweighting to the
driven diffusive lattice gas model. Combining with the dynamical finite-size
scaling theory, we estimate the critical temperature Tc and the dynamical
exponent z. We also argue that this technique has an interesting feature that
enables explicit calculation of derivatives of thermodynamic quantities without
resorting to numerical differences.Comment: Accepted for publication in J. Phys. A (Lett.
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