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Center for Nonlinear Studies |
Presentation of a planned project for exploring renormalization trajectories in models on the body-centered hyper-cubic lattice (D4) using methods developed by Gupta and Cordery based on starting from a guessed renormalized Hamiltonian. Advantages of the D4 lattice and the guessed Hamiltonian methods will be presented. There are a large number of coefficients in the Hamiltonian even for loops of length up to four. The basic plaquette on D4 is a triangle. There are a number of loops of length four including squares and various combinations of two triangles. The renormalized coefficients are found by a Monte Carlo simulation of a system including the original variables and a guessed Hamiltonian for the block variables. The D4 lattice has many nice features for use in renormalization group. It is a dense-packed lattice with high symmetry. Each site has 24 nearest neighbors. A block consisting of a site and its 8 nearest neighbors along four orthogonal directions can tile D4 with centers on a D4 lattice with nearest neighbor distance. A site and its 24 nearest neighbors can tile D4 with centers on a D4 lattice with nearest neighbor distance. The complicated geometry and proper accounting for all loops in the action is simplified by recognizing D4 as the Hurwitz quaternion integers.
Host: Rajan Gupta