Non-Local Finite-Size Effects in the Dimer Model

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$, and show that, because of certain non-local features present in the model, a change of parity of $N$ induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Rectification of energy and motion in non-equilibrium parity violating metamaterials

Uncovering new mechanisms for rectification of stochastic fluctuations has been a longstanding problem in non-equilibrium statistical mechanics. Here, using a model parity violating metamaterial that is allowed to interact with a bath of active energy consuming particles, we uncover new mechanisms for rectification of energy and motion. Our model active metamaterial can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and inter-particle interactions of the parity violating material can couple with the non-equilibrium fluctuations of an active bath and enable rectification of energy and motion.Comment: 9 Pages + S

The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates

In this paper we generalize the target zone exchange rate as model formalized by Krugman (1988b) to include finite-sized interventions in defense of the zone. The main contributions of these pages consist of linking the recent developments in the theory of target zones to the mirror-image theory of speculative attacks on asset price fixing regimes and in using aspects of that linkage to give an intuitive interpretation to the smooth pasting" condition usually invoked as a terminal condition.

Japanese monetary policy, 1991-2001

Monetary policy

Schnyder decompositions for regular plane graphs and application to drawing

Schnyder woods are decompositions of simple triangulations into three edge-disjoint spanning trees crossing each other in a specific way. In this article, we define a generalization of Schnyder woods to $d$-angulations (plane graphs with faces of degree $d$) for all $d\geq 3$. A \emph{Schnyder decomposition} is a set of $d$ spanning forests crossing each other in a specific way, and such that each internal edge is part of exactly $d-2$ of the spanning forests. We show that a Schnyder decomposition exists if and only if the girth of the $d$-angulation is $d$. As in the case of Schnyder woods ($d=3$), there are alternative formulations in terms of orientations ("fractional" orientations when $d\geq 5$) and in terms of corner-labellings. Moreover, the set of Schnyder decompositions on a fixed $d$-angulation of girth $d$ is a distributive lattice. We also show that the structures dual to Schnyder decompositions (on $d$-regular plane graphs of mincut $d$ rooted at a vertex $v^*$) are decompositions into $d$ spanning trees rooted at $v^*$ such that each edge not incident to $v^*$ is used in opposite directions by two trees. Additionally, for even values of $d$, we show that a subclass of Schnyder decompositions, which are called even, enjoy additional properties that yield a reduced formulation; in the case d=4, these correspond to well-studied structures on simple quadrangulations (2-orientations and partitions into 2 spanning trees). In the case d=4, the dual of even Schnyder decompositions yields (planar) orthogonal and straight-line drawing algorithms. For a 4-regular plane graph $G$ of mincut 4 with $n$ vertices plus a marked vertex $v$, the vertices of $G\backslash v$ are placed on a $(n-1) \times (n-1)$ grid according to a permutation pattern, and in the orthogonal drawing each of the $2n-2$ edges of $G\backslash v$ has exactly one bend. Embedding also the marked vertex $v$ is doable at the cost of two additional rows and columns and 8 additional bends for the 4 edges incident to $v$. We propose a further compaction step for the drawing algorithm and show that the obtained grid-size is strongly concentrated around $25n/32\times 25n/32$ for a uniformly random instance with $n$ vertices

Conformal boundary loop models

We study a model of densely packed self-avoiding loops on the annulus, related to the Temperley Lieb algebra with an extra idempotent boundary generator. Four different weights are given to the loops, depending on their homotopy class and whether they touch the outer rim of the annulus. When the weight of a contractible bulk loop x = q + 1/q satisfies -2 < x <= 2, this model is conformally invariant for any real weight of the remaining three parameters. We classify the conformal boundary conditions and give exact expressions for the corresponding boundary scaling dimensions. The amplitudes with which the sectors with any prescribed number and types of non contractible loops appear in the full partition function Z are computed rigorously. Based on this, we write a number of identities involving Z which hold true for any finite size. When the weight of a contractible boundary loop y takes certain discrete values, y_r = [r+1]_q / [r]_q with r integer, other identities involving the standard characters K_{r,s} of the Virasoro algebra are established. The connection with Dirichlet and Neumann boundary conditions in the O(n) model is discussed in detail, and new scaling dimensions are derived. When q is a root of unity and y = y_r, exact connections with the A_m type RSOS model are made. These involve precise relations between the spectra of the loop and RSOS model transfer matrices, valid in finite size. Finally, the results where y=y_r are related to the theory of Temperley Lieb cabling.Comment: 28 pages, 19 figures, 2 tables. v2: added new section 3.2, amended figures 17-18, updated reference

"The Nature and Role of Monetary Policy When Money Is Endogenous"

This paper considers the nature and role of monetary policy when money is envisaged as credit money endogenously created within the private sector (by the banking system). Monetary policy is now based in many countries on the setting (or targeting) of a key interest rate, such as the Central Bank discount rate. The amount of money in existence then arises from the interaction of the private sector and the banks, based on the demand to hold money and the willingness of banks to provide loans. Monetary policy has become closely linked with the targeting of the rate of inflation. In this paper we consider whether monetary policy is well-equipped to act as a counter-inflation policy and discuss the more general role of monetary policy in the context of the treatment of money as endogenous. Currently, two schools of thought view money as endogenous. One school has been labeled the "new consensus" and the other the Keynesian endogenous (bank) money approach. Significant differences exist between the two approaches; the most important of these, for the purposes of this paper, is in the way in which the endogeneity of money is viewed. Although monetary policy--essentially interest rate policy--appears to be the same in both schools of thought, it is not. In this paper we investigate the differing roles of monetary policy in these two schools.