Simplicial Chiral Models

Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix systems in the double scaling limit are discussed.Comment: 6 pages, PHYZZ

Idealized Multigrid Algorithm for Staggered Fermions

An idealized multigrid algorithm for the computation of propagators of staggered fermions is investigated. Exemplified in four-dimensional $SU(2)$ gauge fields, it is shown that the idealized algorithm preserves criticality under coarsening. The same is not true when the coarse grid operator is defined by the Galerkin prescription. Relaxation times in computations of propagators are small, and critical slowing is strongly reduced (or eliminated) in the idealized algorithm. Unfortunately, this algorithm is not practical for production runs, but the investigations presented here answer important questions of principle.Comment: 11 pages, no figures, DESY 93-046; can be formatted with plain LaTeX article styl

Hybrid Monte Carlo Simulation of Graphene on the Hexagonal Lattice

We present a method for direct hybrid Monte Carlo simulation of graphene on the hexagonal lattice. We compare the results of the simulation with exact results for a unit hexagonal cell system, where the Hamiltonian can be solved analytically.Comment: 5 pages, 4 figure

Green's Functions from Quantum Cluster Algorithms

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.Comment: 15 pages, LaTeX, with four figures. Added preprint numbe

Representation of the Human Musculature in the Bronze Age Aegean

Bronze Age sculptures range from abstract to realistic, but how accurate are the realistic sculptures? To answer this question, it is useful to compare three pieces of artwork: Prince of Lilies from Knossos, Kouros from Palaikastro, and the Boxer Rhyta from Ayia Triadha to a musculature replica. These pieces originate from the Bronze Age in the Aegean. What this comparison will tell us is how much the ancient peoples were studying the human body, along with the reasons as to why these sculptures were portrayed with such realistic characteristics. To accomplish this goal this paper takes the artifacts background into consideration, while measuring the length of several muscle groups and comparing them to an anatomical representation. The results showed varied accuracy with how the artifacts compare to anatomical models. One of the artifacts is shown to be almost identical to the anatomical replica. Other conclusions involve the backgrounds of the sculptures which range from religious reasons to possible images of royalty. Each provides insight into the life of the Bronze Age Aegean. In addition, a further study into the Prince of Lilies from Knossos, showed that the artifact was reconstructed, and that there are some controversies surrounding the reconstruction

Spin-String Interaction in QCD Strings

I consider the question of the interaction between a QCD string and the spin of a quark or an antiquark on whose worldline the string terminates. The problem is analysed from the point of view of a string representation for the expectation value of a Wilson loop for a spin-half particle. A string representation of the super Wilson loop is obtained starting from an effective string representation of a Wilson Loop. The action obtained in this manner is invariant under a worldline supersymmetry and has a boundary term which contains the spin-string interaction. For rectangular loops the spin-string interaction vanishes and there is no spin-spin term in the resulting heavy quark potential. On the other hand if an allowance is made for the finite intrinsic thickness of the flux-tube, by assuming that the spin-string interaction takes place not just at the boundary of the string world-sheet but extends to a distance of the order of the intrinsic thickness of the flux tube, then we do obtain a spin-spin interaction which falls as the fifth power of the distance. Such a term was previously suggested by Kogut and Parisi in the context of a flux-tube model of confinement.Comment: 19 pages, 1 figure; Published version with added discussion and references in section