180 research outputs found
Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements
We report several results concerning , the
exponent of the ground state entropy of the Potts antiferromagnet on a lattice
. First, we improve our previous rigorous lower bound on for
the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to
the first eleven terms with the large- series for . Second, we
investigate the heteropolygonal Archimedean lattice, derive a
rigorous lower bound, on , and calculate the large- series
for this function to where . Remarkably, these agree
exactly to all thirteen terms calculated. We also report Monte Carlo
measurements, and find that these are very close to our lower bound and series.
Third, we study the effect of non-nearest-neighbor couplings, focusing on the
square lattice with next-nearest-neighbor bonds.Comment: 13 pages, Latex, to appear in Phys. Rev.
Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
We prove a general rigorous lower bound for
, the exponent of the ground state
entropy of the -state Potts antiferromagnet, on an arbitrary Archimedean
lattice . We calculate large- series expansions for the exact
and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large- expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions for large on the various lattices
. Plots of are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for to be analytic at is that is a regular
lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in
Phys. Rev.
'Worlds of justificationâ in the politics and practices of urban regeneration
A considerable body of research has developed on processes of neoliberal urban regeneration and gentrifi cation. On the one hand, there are many political economy accounts emphasising the role of economic capital in processes of urban change and gentrifi cation. On the other hand, there is a wealth of governmentality studies on the art of government that fail to explain how ungovernable subjects develop. Similarly, within gentrifi cation studies there are many accounts on the role of changing consumer lifestyles and defi ning gentrifi cation, but less concern with the governance processes between actors in urban regeneration and gentrifi cation. Yet such issues are of considerable importance given the role of the state in urban regeneration and dependence on private capital. This paper utilises the French Pragmatist approach of Boltanski and ThĂ©venot to examine a case study state-led gentrifi cation project. Boltanski and ThĂ©venot argue that social coordination occurs by way of actors working through broader value-laden âworlds of justifi cationâ that underpin processes of argumentation and coordination. The examined case study is a deprived area within an English city where a major state-led gentrification programme has been introduced. The rationale for the programme is based on the assumption that reducing deprivation relies upon substantially increasing the number of higher income earners. The paper concludes that market values have overridden broader civic values in the negotiation process, with this intensifying as the state internalised market crisis tendencies within the project. More broadly, there is a need for French Pragmatism to be more sensitive to the spatial processes of social coordination, which can be achieved through critical engagement with recent concepts of âassemblagesâ
Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet
The Ising-like spin ice model, with a macroscopically degenerate ground
state, has been shown to be approximated by several real materials. Here we
investigate a model related to spin ice, in which the Ising spins are replaced
by classical Heisenberg spins. These populate a cubic pyrochlore lattice and
are coupled to nearest neighbours by a ferromagnetic exchange term J and to the
local axes by a single-ion anisotropy term D. The near neighbour spin
ice model corresponds to the case D/J infinite. For finite D/J we find that the
macroscopic degeneracy of spin ice is broken and the ground state is
magnetically ordered into a four-sublattice structure. The transition to this
state is first-order for D/J > 5 and second-order for D/J < 5 with the two
regions separated by a tricritical point. We investigate the magnetic phase
diagram with an applied field along [1,0,0] and show that it can be considered
analogous to that of a ferroelectric.Comment: 7 pages, 4 figure
Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
We study the asymptotic limiting function , where is the chromatic polynomial for a graph
with vertices. We first discuss a subtlety in the definition of
resulting from the fact that at certain special points , the
following limits do not commute: . We then
present exact calculations of and determine the corresponding
analytic structure in the complex plane for a number of families of graphs
, including circuits, wheels, biwheels, bipyramids, and (cyclic and
twisted) ladders. We study the zeros of the corresponding chromatic polynomials
and prove a theorem that for certain families of graphs, all but a finite
number of the zeros lie exactly on a unit circle, whose position depends on the
family. Using the connection of with the zero-temperature Potts
antiferromagnet, we derive a theorem concerning the maximal finite real point
of non-analyticity in , denoted and apply this theorem to
deduce that and for the square and
honeycomb lattices. Finally, numerical calculations of and
are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes
further comments on large-q serie
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X-ray microscopy using collimated and focussed synchrotron radiation
X-ray microscopy is a field that has developed rapidly in recent years. Two different approaches have been used. Zone plates have been employed to produce focused beams with sizes as low as 0.07 ..mu..m for x-ray energies below 1 keV. Images of biological materials and elemental maps for major and minor low Z have been produced using above and below absorption edge differences. At higher energies collimators and focusing mirrors have been used to make small diameter beams for excitation of characteristic K- or L-x rays of all elements in the periodic table. The practicality of a single instrument combining all the features of these two approaches is unclear. The use of high-energy x rays for x-ray microscopy has intrinsic value for characterization of thick samples and determination of trace amounts of most elements. A summary of work done on the X-26 beam line at the National Synchrotron Light Source (NSLS) with collimated and focused x rays with energies above 4 keV is given here. 6 refs., 5 figs., 1 tab
Elementary chemical analysis in leaves infected by fumagina by X-Ray fluorescence technique
Professionalisation of sport federations â a multi-level framework for analysing forms, causes and consequences
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Recent Results Using Synchrotron Radiation for Energy Dispersive X-Ray Fluorescence Analysis
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