A System Exhibiting Toroidal Order

A two dimensional system of discs upon which a triangle of spins are mounted is shown to undergo a sequence of interesting phase transitions as the temperature is lowered. We are mainly concerned with the `solid' phase in which bond orientational order but not positional order is long ranged. As the temperature is lowered in the `solid' phase, the first phase transition involving the orientation or toroidal charge of the discs is into a `gauge toroid' phase in which the product of a magnetic toroidal parameter and an orientation variable (for the discs) orders but due to a local gauge symmetry these variables themselves do not individually order. Finally, in the lowest temperature phase the gauge symmetry is broken and toroidal order and orientational order both develop. In the `gauge toroidal' phase time reversal invariance is broken and in the lowest temperature phase inversion symmetry is also broken. In none of these phases is there long range order in any Fourier component of the average spin. A definition of the toroidal magnetic moment $T_i$ of the $i$th plaquette is proposed such that the magnetostatic interaction between plaquettes $i$ and $j$ is proportional to $T_iT_j$. Symmetry considerations are used to construct the magnetoelectric free energy and thereby to deduce which coefficients of the linear magnetoelectric tensor are allowed to be nonzero. In none of the phases does symmetry permit a spontaneous polarization.Comment: 9 pages, 6 figure

Livingstone versus Serota: the High-rise Battle of Bankside

In 2001, plans were unveiled by a private developer for a 32-storey residential tower next to the Tate Gallery of Modern Art in Bankside. Although not the tallest building proposed within London's high-rise landscape, this tower became a minor cause célèbre within the city's media. The twists and turns involved in attempts to win — and oppose — planning permission for the building are charted in this paper. Yet, the vociferous battle involved does not reveal distinct political and social fault-lines. Instead, it highlights how an agenda of corporate property-led development has come to dominate efforts to regenerate and re-imagine contemporary London

The Reality of Racial Disparity in Criminal Justice: The Significance of Data Collection

Criminologists have long debated the presence of racial disparity at various places in the criminal justice system, from initial on-the-street encounters between citizens and police officers to the sentencing behavior of judges. What is new is the use of statistics designed to persuade the public, and not just other academics and researchers, that grave racial disparities exist in the system, and that these disparities necessitate significant policy changes

BES Results on Charmonium Decays and Transitions

Results are reported based on samples of 58 million $J/\psi$ and 14 million $\psi(2S)$ decays obtained by the BESII experiment. Improved branching fraction measurements are determined, including branching fractions for $J/\psi\to\pi^+\pi^-\pi^0$, $\psi(2S)\to \pi^0 J/\psi$, $\eta J/\psi$, $\pi^0 \pi^0 J/\psi$, anything $J/\psi$, and \psi(2S)\to\gamma\chi_{c1},\gamma\chi_{c2}\to\gamma\gamma\jpsi. Using 14 million $\psi(2S)$ events, $f_0(980)f_0(980)$ production in $\chi_{c0}$ decays and $K^*(892)^0\bar K^*(892)^0$ production in $\chi_{cJ}~(J=0,1,2)$ decays are observed for the first time, and branching ratios are determined.Comment: Parallel Talk presented at ICHEP04. 4 pages and 6 figure

Unbounded Symmetric Homogeneous Domains in Spaces of Operators

We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville's theorem holds for domains of linear fractional transformations, and, with an additional trace class condition, so does the Riemann removable singularities theorem. We also show that every biholomorphic mapping of the operator domain $I < Z^*Z$ is a linear isometry when the space of operators is a complex Jordan subalgebra of ${\cal L}(H)$ with the removable singularity property and that every biholomorphic mapping of the operator domain $I + Z_1^*Z_1 < Z_2^*Z_2$ is a linear map obtained by multiplication on the left and right by J-unitary and unitary operators, respectively. Readers interested only in the finite dimensional case may identify our spaces of operators with spaces of square and rectangular matrices

Landau Theory of Tilting of Oxygen Octahedra in Perovskites

The list of possible commensurate phases obtained from the parent tetragonal phase of Ruddlesden-Popper systems, A$_{n+1}$B$_n$C$_{3n+1}$ for general $n$ due to a single phase transition involving the reorienting of octahedra of C (oxygen) ions is reexamined using a Landau expansion. This expansion allows for the nonlinearity of the octahedral rotations and the rotation-strain coupling. It is found that most structures allowed by symmetry are inconsistent with the constraint of rigid octahedra which dictates the form of the quartic terms in the Landau free energy. For A$_2$BC$_4$ our analysis allows only 10 (see Table III) of the 41 structures listed by Hatch {\it et al.} which are allowed by general symmetry arguments. The symmetry of rotations for RP systems with $n>2$ is clarified. Our list of possible structures in Table VII excludes many structures allowed in previous studies.Comment: 21 pages, 21 figures. An elaboration of arXiv:1012.512