Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Lectures on Superstring Phenomenology

The phenomenological aspects of string theory are briefly reviewed. Emphasis is given to the status of 4D string model building, effective Lagrangians, model independent results, supersymmetry breaking and duality symmetries.Comment: 41 pages, latex, given at V Latin American Workshop on Particles and Fields, Mexico, 1995 (typos corrected, a footnote changed and more references added

Calabi-Yau threefolds with large h^{2, 1}

We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section ("EFS") and have a large Hodge number h^{2, 1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space associated with different topologies connected through transitions that can be understood in terms of singular Weierstrass models. We determine the complete set of such threefolds that have h^{2, 1} >= 350 by tuning coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2, 1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate that there are no other Calabi-Yau threefolds (elliptically fibered or not) with Hodge numbers that exceed this bound. We summarize the theoretical and practical obstacles to a complete enumeration of all possible EFS Calabi-Yau threefolds and fourfolds, including those with small Hodge numbers, using this approach.Comment: 44 pages, 5 tables, 5 figures; v2: minor corrections; v3: minor corrections, moved figure; v4: typo in Table 2 correcte