The arctic curve of the domain-wall six-vertex model

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of $q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction

Fermionic Quantum Gravity

We study the statistical mechanics of random surfaces generated by NxN one-matrix integrals over anti-commuting variables. These Grassmann-valued matrix models are shown to be equivalent to NxN unitary versions of generalized Penner matrix models. We explicitly solve for the combinatorics of 't Hooft diagrams of the matrix integral and develop an orthogonal polynomial formulation of the statistical theory. An examination of the large N and double scaling limits of the theory shows that the genus expansion is a Borel summable alternating series which otherwise coincides with two-dimensional quantum gravity in the continuum limit. We demonstrate that the partition functions of these matrix models belong to the relativistic Toda chain integrable hierarchy. The corresponding string equations and Virasoro constraints are derived and used to analyse the generalized KdV flow structure of the continuum limit.Comment: 59 pages LaTeX, 1 eps figure. Uses epsf. References and acknowledgments adde

Post-capitalist property

When writing about property and property rights in his imagined post-capitalist society of the future, Marx seemed to envisage ‘individual property’ co-existing with ‘socialized property’ in the means of production. As the social and political consequences of faltering growth and increasing inequality, debt and insecurity gradually manifest themselves, and with automation and artificial intelligence lurking in the wings, the future of capitalism, at least in its current form, looks increasingly uncertain. With this, the question of what property and property rights might look like in the future, in a potentially post-capitalist society, is becoming ever more pertinent. Is the choice simply between private property and markets, and public (state-owned) property and planning? Or can individual and social property in the (same) means of production co-exist, as Marx suggested? This paper explores ways in which they might, through an examination of the Chinese household responsibility system (HRS) and the ‘fuzzy’ and seemingly confusing regime of land ownership that it instituted. It examines the HRS against the backdrop of Marx’s ideas about property and subsequent (post-Marx) theorizing about the legal nature of property in which property has come widely to be conceptualized not as a single, unitary ‘ownership’ right to a thing (or, indeed, as the thing itself) but as a ‘bundle of rights’. The bundle-of-rights idea of property, it suggests, enables us to see not only that ‘individual’ and ‘socialized’ property’ in the (same) means of production might indeed co-exist, but that the range of institutional possibility is far greater than that between capitalism and socialism/communism as traditionally conceived

The bii4africa dataset of faunal and floral population intactness estimates across Africa’s major land uses

Sub-Saharan Africa is under-represented in global biodiversity datasets, particularly regarding the impact of land use on species’ population abundances. Drawing on recent advances in expert elicitation to ensure data consistency, 200 experts were convened using a modified-Delphi process to estimate ‘intactness scores’: the remaining proportion of an ‘intact’ reference population of a species group in a particular land use, on a scale from 0 (no remaining individuals) to 1 (same abundance as the reference) and, in rare cases, to 2 (populations that thrive in human-modified landscapes). The resulting bii4africa dataset contains intactness scores representing terrestrial vertebrates (tetrapods: ±5,400 amphibians, reptiles, birds, mammals) and vascular plants (±45,000 forbs, graminoids, trees, shrubs) in sub-Saharan Africa across the region’s major land uses (urban, cropland, rangeland, plantation, protected, etc.) and intensities (e.g., large-scale vs smallholder cropland). This dataset was co-produced as part of the Biodiversity Intactness Index for Africa Project. Additional uses include assessing ecosystem condition; rectifying geographic/ taxonomic biases in global biodiversity indicators and maps; and informing the Red List of Ecosystems