A technique for analytical calculation of observables in lattice gauge theories

Abstract

It is shown that the partition function for a finite lattice factorizes into terms that can be associated with each vertex in the finite lattice. This factorization property forms the basis of a well defined and efficient technique developed to calculate partition functions to high accuracy, on finite lattices for gauge theories. This technique along with the expansion in finite lattices of ref. 2, provides a powerful means for calculating observables in lattice gauge theories. This is applied to SU(2) lattice gauge theory in four dimensions. The free energy, expectation value of a plaquette and specific heat are calculated. The results are very good in the strong coupling region, succeed in entering the weak couplinh region and describe the crossover region quite well, agreeing all the way with the Monte Carlo data.