Decay of the metastable phase in d=1 and d=2 Ising models

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.Comment: 4 pages, REVTe

Foreword to Supplement 1: research on a polar species—the Arctic fox

The Arctic fox has a circumpolar distribution and is intensively studied because it is adapted to extreme environments and influences the ecology of many other species. We introduce here a collection of 12 articles on Arctic fox biology and management. After summarizing the main biological features of the species, we explore the peer-reviewed literature dealing with the Arctic fox through a bibliometric network analysis which identifies clusters of papers sharing a high similarity of cited literature. We visualize with a word cloud analysis 10 clusters comprising 97% of 755 articles published by 1742 authors from 1996–2015. Behavioural and ecological questions, including conservation science, dominate this recent literature. The collection of papers published in the supplement offers an excellent representation of current research dealing with Arctic fox biology and management