Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Global Monte Carlo for fermions using ordered statistics

In this talk I discuss a new possibility for stochastic representation of the fe rmion determinant. The method can be used for global Monte Carlo fermion algorit hms and is tested in the case of the Schwinger model.Comment: 3 pages, Lattice2003 (Machines I

Universality in Two Dimensional Gauge Theory.

We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the detailed structure of the model, and only depends on the gauge group $G$ and an integer $k$ measuring the total anomaly. The massless physics, which does depend on the details of the model, decouples (almost) completely from that of the massive one. As an example, we discuss the equivalence of QCD$_2$ coupled to fermions in the adjoint, and fundamental representations.Comment: 16 pages, harvma

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767

Electrochemistry and Spectroscopy of a Molybdenum Porphyrin Compound

Carbon dioxide has been a problematic greenhouse gas since the beginning of the industrial age. In an effort to remediate its effects on the climate, multiple techniques have been utilized in the chemical and electrochemical reduction of CO2. Homogeneous electrocatalysis for carbon dioxide reduction has been a topic of increasing interest. However, a full examination of the catalytic performance of early transition metals supported by macroligands has yet to be done. The research reported involves synthesis of a chelate of molybdenum within a tetraphenylporphyrin, and then synthesis, purification, and characterization of its ability to reduce carbon dioxide. The complex was found to be air-stable and robust. However, it was paramagnetic and not found to be an efficient electrocatalyst for CO2 reduction

The Role of Temperature in a Dimensional Approach to QCD_3

We analyze the role played by temperature in QCD_3 by means of a dimensional interpolating approach. Pure gauge QCD_3 is defined on a strip of finite width L, which acts as an interpolating parameter between two and three dimensions. A two-dimensional effective theory can be constructed for small enough widths giving the same longitudinal physics as QCD_3. Explicit calculations of T-dependent QCD_3 observables can thus be performed. The generation of a deconfinig phase transition, absent in QCD_2, is proven through an exact calculation of the electric or Debye mass at high T. Low and high T behaviors of relevant thermodynamic functions are also worked out. An accurate estimate of the critical temperature is given and its evolution with L is studied in detail.Comment: 27 pages, 3 postscript figures. Changes in section

Mesonic Spectra of Bosonized QCD_2 Models

We discuss bosonized two-dimensional QCD with massless fermions in the adjoint and multi-flavor fundamental representations. We evaluate the massive mesonic spectra of several models by using the light-front quantization and diagonalizing the mass operator $M^2=2P^+P^-$. We recover previous results in the case of one flavor adjoint fermions and we find the exact massive spectrum of multi flavor QCD in the limit of large number of flavors.Comment: 17 pages, Late

Phase structure and monopoles in U(1) gauge theory

We investigate the phase structure of pure compact U(1) lattice gauge theory in 4 dimensions with the Wilson action supplemented by a monopole term. To overcome the suppression of transitions between the phases in the simulations we make the monopole coupling a dynamical variable. We determine the phase diagram and find that the strength of the first order transition decreases with increasing weight of the monopole term, the transition thus ultimately getting of second order. After outlining the appropriate topological characterization of networks of currents lines, we present an analysis of the occurring monopole currents which shows that the phases are related to topological properties.Comment: 22 pages (latex), 14 figures (available upon request), BU-HEP 94-

On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where $N$ is an $n$-dim internal space (Cho, Sho, Park, Yoon). Based on these findings, a very plausible geometrical interpretation of the $AdS/CFT$ correspondence could be given. Conformally invariant sigma models in $D=2n$ dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the non-compact nature of the SO(2n,1), the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal ``stereographic'' mappings of $R^{2n}$ into the Euclidean signature $AdS_{2n}$ spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on $W_\infty$ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in $AdS_4$. This $AdS_4$ spacetime higher spin theory should have a one-to-one correspondence to noncritical $W_\infty$ strings propagating on $AdS_4 \times S^7$.Comment: 43 pages, Tex fil