The order parameter of the chiral Potts model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is aware there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ``broken rapidity line'' approach pioneered by Jimbo, Miwa and Nakayashiki.Comment: 29 pages, 7 figures. Citations made more explicit and some typos correcte

Governing the financial or bank holding company: how legal infrastructure can facilitate consolidated risk management

On October 25, 2002, Thomas C. Baxter, Jr., General Counsel and Executive Vice President of the Federal Reserve Bank of New York, presented the following remarks at the Puerto Rico Bankers Association conference "Financial Transparency and Corporate Governance of Financial Institutions after the Sarbanes-Oxley Act of 2002" in San Juan, Puerto Rico.Corporate governance ; Financial institutions - Law and legislation ; Risk management ; Bank holding companies

Efficient simulation of relativistic fermions via vertex models

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped to statistical vertex models and our proposal is in fact an efficient simulation algorithm for generic vertex models in arbitrary dimensions. The algorithm essentially eliminates critical slowing down by sampling two-point correlation functions and it allows simulations directly in the massless limit. Moreover, it generates loop configurations with fluctuating topological boundary conditions enabling to simulate fermions with arbitrary periodic or anti-periodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.Comment: 5 pages, 4 figure

Some comments on developments in exact solutions in statistical mechanics since 1944

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise

Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalised by the `commuting transfer matrices' method. {}From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on the $XXZ$ spin chain is also discussed.Comment: 18 pages, LaTeX with 1 PostScript figur

Ex-nihilo: Obstacles Surrounding Teaching the Standard Model

The model of the Big Bang is an integral part of the national curriculum for England. Previous work (e.g. Baxter 1989) has shown that pupils often come into education with many and varied prior misconceptions emanating from both internal and external sources. Whilst virtually all of these misconceptions can be remedied, there will remain (by its very nature) the obstacle of ex-nihilo, as characterised by the question `how do you get something from nothing?' There are two origins of this obstacle: conceptual (i.e. knowledge-based) and cultural (e.g. deeply held religious viewpoints). The article shows how the citizenship section of the national curriculum, coming `online' in England from September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E

Gas release and conductivity modification studies

The behavior of gas clouds produced by releases from orbital velocity in either a point release or venting mode is described by the modification of snowplow equations valid in an intermediate altitude regime. Quantitative estimates are produced for the time dependence of the radius of the cloud, the average internal energy, the translational velocity, and the distance traveled. The dependence of these quantities on the assumed density profile, the internal energy of the gas, and the ratio of specific heats is examined. The new feature is the inclusion of the effect of the large orbital velocity. The resulting gas cloud models are used to calculate the characteristics of the field line integrated Pedersen conductivity enhancements that would be produced by the release of barium thermite at orbital velocity in either the point release or venting modes as a function of release altitude and chemical payload weight

A computer solution for the dynamic load, lubricant film thickness, and surface temperatures in spiral-bevel gears

A computer method for determining the dynamic load between spiral bevel pinion and gear teeth contact along the path of contact is described. The dynamic load analysis governs both the surface temperature and film thickness. Computer methods for determining the surface temperature, and film thickness are presented along with results obtained for a pair of typical spiral bevel gears

Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues of the Q-operator is derived. A proof is given for states which contain up to three Bethe roots. Further evidence is provided by relating the findings to the six-vertex fusion hierarchy. For the XXZ spin-chain we analyze the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page

Two-dimensional Rydberg gases and the quantum hard squares model

We study a two-dimensional lattice gas of atoms that are photo-excited to high-lying Rydberg states in which they interact via the van-der-Waals interaction. We explore the regime of dominant nearest neighbor interaction where this system is intimately connected to a quantum version of Baxter's hard squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard squares model. This correspondence allows us to identify a first order phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase