59,259 research outputs found
Bulk and boundary scattering in the q-state potts mode
No full textThis thesis is concerned with the properties of 1 + 1 dimensional massive field theories in both infinite and semi-infinite geometries. Chapters 1, 2 and 3 develop the necessary theoretical framework and review existing work by Chim and Zamolodchikov [1] on integrable perturbations of the (bulk) q-state Potts model, the particular model under consideration in this thesis. Chapter 4 consists of a detailed analysis of the bootstrap for this model, during the course of which unexpected behaviour arises. The treatment of 1] has consequently been revised, but further investigation will be necessary before complete understanding of this behaviour can be reached. In the final chapter, attention turns to the imposition of boundary conditions on two dimensional systems. After looking at this from a statistical mechanical point of view, a brief review of boundary conformal held theory and its integrable perturbations is given. This leads once more to a consideration of the q-state Potts model. After summarising [2], where fixed and free boundary conditions are considered, a third and previously untreated boundary condition is discussed
Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models
No full textThis letter considers the problem of computing the Cramer–Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models
Bounds on the complex zeros of (Di)Chromatic polynomials and Potts-model partition functions
No full textWe show that there exist universal constants C(r) such that, for all loopless graphs G of maximum degree less than or equal to r, the zeros (real or complex) of the chromatic polynomial P-G(q) lie in the disc \q\ 7.963907r. This result is a corollary of a more general result on the zeros of the Potts-model partition function Z(G)(q. {v(e)}) in the complex antiferromagnetic regime \1 + v(e)\ less than or equal to 1. The proof is based on a transformation of the Whitney-Tutte-Fortuin-Kasteleyn representation of Z(G)(q,:{v(e)}) to a polymer gas. followed by verification of the Dobrushin-Kotecky-Preiss condition for nonvanishing of a polymer-model partition function. We also show that, for all loopless graphs G of second-largest degree less than or equal to r, the zeros of P-G(q) lie in the disc \q\ < C(r)+ 1. Along the way, I give a simple proof of a generalized (multivariate) Brown-Colbourn conjecture on the zeros of the reliability polynomial for the special case of series-parallel graphs
Chromatic roots are dense in the whole complex plane
No full textI show that the zeros of the chromatic polynomials P-G(q) for the generalized theta graphs Theta((s.p)) are taken together, dense in the whole complex plane with the possible exception of the disc \q - l\ < l. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) Z(G)(q,upsilon) outside the disc \q + upsilon\ < \upsilon\. An immediate corollary is that the chromatic roots of not-necessarily-planar graphs are dense in the whole complex plane. The main technical tool in the proof of these results is the Beraha-Kahane-Weiss theorem oil the limit sets of zeros for certain sequences of analytic functions, for which I give a new and simpler proof
Une synthèse sur les mentalités religieuses en Normandie au XIe siècle. Dr J. Fournée, Les mentalités religieuses au XIe siècle en Normandie, 1988
No full textPotts Cassandra. Une synthèse sur les mentalités religieuses en Normandie au XIe siècle. Dr J. Fournée, Les mentalités religieuses au XIe siècle en Normandie, 1988. In: Études Normandes, 37e année, n°4, 1988. Images d'histoire normande. p. 75
Measurement of the ratio of prompt χ c to J / ψ production in pp collisions at √s = 7 TeV
No full textThe prompt production of charmonium χ c and J / ψ states is studied in proton-proton collisions at a centre-of-mass energy of √s = 7 TeV at the Large Hadron Collider. The χ c and J / ψ mesons are identified through their decays χ c → J / ψ γ and J / ψ → μ + μ - using 36 pb - 1 of data collected by the LHCb detector in 2010. The ratio of the prompt production cross-sections for χ c and J / ψ, σ (χ c → J / ψ γ) / σ (J / ψ), is determined as a function of the J / ψ transverse momentum in the range 2 < p T J / ψ < 15 GeV / c. The results are in excellent agreement with next-to-leading order non-relativistic expectations and show a significant discrepancy compared with the colour singlet model prediction at leading order, especially in the low p T J / ψ region
Phase transitions in the Potts spin-glass model
No full textWe have studied the Potts spin glass with two-state Ising spins and
s
-state Potts variables using a cluster Monte Carlo dynamics. The model recovers the
±
J
Ising spin glass (SG) for
s
=
1
and exhibits for all
s
a SG transition at
T
SG
(
s
)
and a percolation transition at higher temperature
T
p
(
s
)
.
We have shown that for all values of
s
≠
1
at
T
p
(
s
)
there is a thermodynamic transition in the universality class of a ferromagnetic
s
-state Potts model. The efficiency of the cluster dynamics is compared with that of standard spin-flip dynamics
On Gibbs measures of P-adic Potts model on the cayley tree
No full textAbstractWe consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ϵ Qp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ϵ pN and p ≥ 3 (resp. q ϵ 22N, p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ϵ pN if p ≥ 3 and q ϵ 22N if p = 2
Occidental and oriental elements in the religions of Babylonia and Iran during the Third and Second Centuries B. C. : P. Bilde, T. Engberg-Pedersen, L. Hannestad and J. Zahle, Religion and Religious Practice in the Seleucid Kingdom, 1990
No full textPotts Daniel T. Occidental and oriental elements in the religions of Babylonia and Iran during the Third and Second Centuries B. C. : P. Bilde, T. Engberg-Pedersen, L. Hannestad and J. Zahle, Religion and Religious Practice in the Seleucid Kingdom, 1990. In: Topoi, volume 3/1, 1993. pp. 345-354
Fifty years of scheduling: a survey of milestones
No full textScheduling has become a major field within operational research with several hundred publications appearing each year. This paper explores the historical development of the subject since the mid 1950s when the landmark publications started to appear. A discussion of the main topics of scheduling research for the past five decades is provided, highlighting the key contributions that helped shape the subject. The main topics covered in the respective decades are combinatorial analysis, branch and bound, computational complexity and classification, approximate solution algorithms, and enhanced scheduling models
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