Dynamics of relaxor ferroelectrics

We study a dynamic model of relaxor ferroelectrics based on the spherical random-bond---random-field model and the Langevin equations of motion. The solution to these equations is obtained in the long-time limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and third-order nonlinear susceptibilities $\chi_1(\omega)$ and $\chi_3(\omega)$, respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in $\chi_3(T,\omega)$, which mimics a transition into a glass-like state.Comment: 15 pages, Revtex plus 5 eps figure

Fanny Copeland and the geographical imagination

Raised in Scotland, married and divorced in the English south, an adopted Slovene, Fanny Copeland (1872 – 1970) occupied the intersection of a number of complex spatial and temporal conjunctures. A Slavophile, she played a part in the formation of what subsequently became the Kingdom of Yugoslavia that emerged from the First World War. Living in Ljubljana, she facilitated the first ‘foreign visit’ (in 1932) of the newly formed Le Play Society (a precursor of the Institute of British Geographers) and guided its studies of Solčava (a then ‘remote’ Alpine valley system) which, led by Dudley Stamp and commended by Halford Mackinder, were subsequently hailed as a model for regional studies elsewhere. Arrested by the Gestapo and interned in Italy during the Second World War, she eventually returned to a socialist Yugoslavia, a celebrated figure. An accomplished musician, linguist, and mountaineer, she became an authority on (and populist for) the Julian Alps and was instrumental in the establishment of the Triglav National Park. Copeland’s role as participant observer (and protagonist) enriches our understanding of the particularities of her time and place and illuminates some inter-war relationships within G/geography, inside and outside the academy, suggesting their relative autonomy in the production of geographical knowledge

Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields (represented by $p_{0}$). The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for $0<p_{0}<p_{0}^{*} \approx 0.30856$, a single tricritical point occurs, whereas if $p_{0}>p_{0}^{*}$ the critical frontier is completely continuous; however, for $p_{0}=p_{0}^{*}$, a fourth-order critical point appears. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight $p_{0}$.Comment: 23pages, 7 ps figure