It is shown that the Coxeter-Todd lattice is the unique strongly perfect lattice in dimension 12.

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of s different (where s is the number of ground states) Gibbs measures.

The ρ, K and φ decay constants and the vector current renormalization factor are studied by using an O(a2) classically-improved, tadpole-improved action. Tree-level calculations are used to show how the classical improvement of the action, involving next-nearest-neighbour timesteps, is transferred to the matrix elements. Simulations are performed on coarse lattices and compared to Wilson result...

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for ...

Our aim in this contribution is to present some illustrations for the claim that already by looking at the ground states of classical lattice models, one may meet some interesting and non-trivial structures.

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to a lattice theory corresponding to a rank c even, self-dual lattice. If c = 24 we prove, among other things, that either V is isomorphic to a lattice theory corresponding...