2008/12/31 by Gemma De las Cuevas, G. De las Cuevas, Wolfgang Dür +5 · 2 citations
Mathematics · Physics and Astronomy · #Abelian group #Gauge theory #Lattice (music) #Lattice gauge theory #Mathematical physics #Mathematics #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Theoretical physics #cond-mat.stat-mech #hep-lat #quant-ph
paper · pdf · doi:10.1103/physrevlett.102.230502
published as Phys.Rev.Lett.102:230502,2009 · Published version. One new figure and some minor changes
openalex publication_date 2009/06/11 · arxiv created 2009/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unifies all classical spin models with apparently very different features in a single complete model. This result is applied to establish a new method to compute the mean-field theory of Abelian discrete LGTs with d > or = 4, and to show that computing the partition function of the 4D Z2 LGT is computationally hard (#P hard). The 4D Z2 LGT is also proved to be approximately complete for Abelian continuous models. The proof uses techniques from quantum information.