Phase diagram of the three-band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d(x)(2)-y(2) and the O p(x) and p(y) orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

Movement and figurality: The circulation diagram and the history of the architectural plan

Knowledge of the plan competes with self-consciousness of experience. The less we are able to understand our spatio-visual experience by the abstract coordinates of the plan, the more we are thrust back into a lived experience of the building in duration. This formula, frequently unacknowledged, has been one of the main precepts of the experientialist modernism which arises out of the picturesque and which stands in critique of classical idealism. One of the paths to critique this formula is by showing that the attention to the experience of the spaces in duration is predicated on obscuring, complicating and weakening the apprehension of the plan as a figure. Another development in the practice of modern planning has been architects using a kind of over-drawing where human circulation diagrams or 'movement lines' are drawn expressively across the orthographic plane; thus representing the lived experience of buildings. We will show that these two issues are linked; the plan's weak figure and the privilege this supposes for durational experience has a corollary - experience itself demands to be visible in the plan, and this is one origin of the present fascination with 'diagramming'. In this paper we explore the practice of architectural planning and its theoretical underpinnings in an attempt to show the viability of a history of architectural planning methods.