Mahler measures, elliptic curves, and L-functions for the free energy of the Ising model.

This work establishes links between the Ising model and elliptic curves via Mahler measures. First, we reformulate the partition function of the Ising model on the square, triangular, and honeycomb lattices in terms of the Mahler measure of a Laurent polynomial whose variety's projective closure defines an elliptic curve. Next, we obtain hypergeometric formulas for the partition functions on the triangular and honeycomb lattices and review the known series for the square lattice.

Intermediate statistics: Addressing the thermoelectric properties of solids.

We study the thermodynamics of a crystalline solid by applying intermediate statistics obtained by deforming known solid state models using the mathematics of q analogs. We apply the resulting q deformation to both the Einstein and Debye models and study the deformed thermal and electrical conductivities and the deformed Debye specific heat. We find that the q deformation acts in two different ways-but not necessarily as independent mechanisms.

Cause, Consequence, and Control of Ag Vacancies in BaAgAs.

The impact of transition metal (Ag) deficiencies on the structural and transport properties of ThCrSi-type arsenides are investigated. We experimentally confirm a partial occupancy of Ag in BaAgAs, which can be predictably controlled within 0.053(5) ≤ ≤ 0.

Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices.

The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable-or, to be more precise, that there are no differentiably finite (D-finite) solutions.