Algebraic reduction of the Ising model

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.Comment: 25 pages, one figure, last reference completed. Various typos fixed. Changes on 12 July 2008: Fig 1, 0 to +1; before (2.1), if to is; after (4.6), from to form; before (4.46), first three to middle two; before (4.46), last to others; Conclusions, 2nd para, insert how ; renewcommand \i to be \rm

The use of perfluoroether lubricants in unprotected space environments

A series of ball bearing tests in simulated space environment are described which determine durability of perfluoroether lubricants. The results of the examination of the test bearings for each stage are described and experimental techniques designed to overcome lubricant degradation are outlined

The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin chain but their role is similar

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

Spectral characteristics of earth-space paths at 2 and 30 FHz

Spectral characteristics of 2 and 30 GHz signals received from the Applications Technology Satellite-6 (ATS-6) are analyzed in detail at elevation angles ranging from 0 deg to 44 deg. The spectra of the received signals are characterized by slopes and break frequencies. Statistics of these parameters are presented as probability density functions. Dependence of the spectral characteristics on elevation angle is investigated. The 2 and 30 GHz spectral shapes are contrasted through the use of scatter diagrams. The results are compared with those predicted from turbulence theory. The average spectral slopes are in close agreement with theory, although the departure from the average value at any given elevation angle is quite large

Tetromino tilings and the Tutte polynomial

We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polynomial Z\_G(Q,v) (known also to physicists as the partition function of the Q-state Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure

Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions

We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colorability of the lattices to ensure the existence of a crystallization transition. We first solve explicitly the naive (colorless) random-lattice version of the hard-square model and find that the only matter critical point is the non-unitary Lee-Yang edge singularity. We then show how to restore the crystallization transition of the hard-square model by considering the same model on bicolored random lattices. Solving this model exactly, we show moreover that the crystallization transition point lies in the universality class of the Ising model coupled to 2D quantum gravity. We finally extend our analysis to a new two-particle exclusion model, whose regular lattice version involves hard squares of two different sizes. The exact solution of this model on bicolorable random lattices displays a phase diagram with two (continuous and discontinuous) crystallization transition lines meeting at a higher order critical point, in the universality class of the tricritical Ising model coupled to 2D quantum gravity.Comment: 48 pages, 13 figures, tex, harvmac, eps

Non perturbative Adler-Bardeen Theorem

The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.Comment: 28 pages, 14 figure

Critical interfaces and duality in the Ashkin Teller model

We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d_f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.Comment: 5 pages, 4 figure

Critical Exponents of the Four-State Potts Model

The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page