Exact blocking formulas for spin and gauge models
High Energy Physics - Lattice
2014-12-18 v1 Statistical Mechanics
High Energy Physics - Theory
Abstract
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models (the O(2) and O(3) sigma models and the SU(2) principal chiral model) and for the 3D gauge theories with groups Z_2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.
Cite
@article{arxiv.1307.6543,
title = {Exact blocking formulas for spin and gauge models},
author = {Yuzhi Liu and Y. Meurice and M. P. Qin and J. Unmuth-Yockey and T. Xiang and Z. Y. Xie and J. F. Yu and Haiyuan Zou},
journal= {arXiv preprint arXiv:1307.6543},
year = {2014}
}
Comments
12 pages, 10 figures