Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. 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.

'Worlds of justification’ 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 Thévenot to examine a case study state-led gentrifi cation project. Boltanski and Thévenot argue that social coordination occurs by way of actors working through broader value-laden ‘worlds of justifi cation’ 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 ‘assemblages’

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 $W({G},q) = \lim_{n \to \infty}P(G,q)^{1/n}$, where $P(G,q)$ is the chromatic polynomial for a graph $G$ with $n$ vertices. We first discuss a subtlety in the definition of $W({G},q)$ resulting from the fact that at certain special points $q_s$, the following limits do not commute: $\lim_{n \to \infty} \lim_{q \to q_s} P(G,q)^{1/n} \ne \lim_{q \to q_s} \lim_{n \to \infty} P(G,q)^{1/n}$. We then present exact calculations of $W({G},q)$ and determine the corresponding analytic structure in the complex $q$ plane for a number of families of graphs ${G}$, 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 $P(G,q)$ with the zero-temperature Potts antiferromagnet, we derive a theorem concerning the maximal finite real point of non-analyticity in $W({G},q)$, denoted $q_c$ and apply this theorem to deduce that $q_c(sq)=3$ and $q_c(hc) = (3+\sqrt{5})/2$ for the square and honeycomb lattices. Finally, numerical calculations of $W(hc,q)$ and $W(sq,q)$ 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

Differentiation of ceramic chemical element composition and vessel morphology at a pottery production center in Roman Galilee

Cooking pots and bowls from two production locations ca. 200 m from each other at the rural settlement of Kefar Hananya in Roman Galilee were compared employing chemicalelementcomposition and vessel-shape analyses. Splits of each pulverized sample, all of which were taken from ceramic wasters, were analyzed by both instrumental neutron activation and high-precision X-ray fluorescence analyses, and computerized vessel-shape analysis was employed for morphological analysis of the same vessel forms from each location. Several statistical techniques (bivariate plots, principal component analysis, cluster analysis and discriminant analysis) were used for analyzing the resultant data. It was found that both the cooking pots and bowls made at each location could be distinguished by employing either chemicalcomposition or morphological analysis. The implications of this work, with regard to investigating both production and consumption sites, and for pottery provenance studies, are discussed. The findings suggest that these analytical techniques can be useful as an aid for chronological differentiations of archaeological pottery