Unifying all classical spin models in a Lattice Gauge Theory
| Autor: | Cuevas, G. De las, Dür, W., Briegel, H. J., Martin-Delgado, M. A. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Phys.Rev.Lett.102:230502,2009 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.102.230502 |
| Popis: | We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d>3, and we show that the computation of the partition function of the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z_2 LGT. All results are proven using quantum information techniques. Comment: Published version. One new figure and some minor changes |
| Databáze: | arXiv |
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