Construction of the partition function for lattice gauge theory

We review a new method to study lattice simulations of a gauge theory. The method is based on a direct numerical construction of the partition function of the system by computing its spectral density function. This leads to a knowledge of the partition function for a large range of couplings simultaniously including couplings that are complex. This allows for a study of various properties of the system which includes locating phase transitions as well as the determination of their critical exponents using the finite size scaling properties of the relevant nearest zeros of the partition function in the complex coupling plane. We restrict our discussion here to SU(2) lattice gauge theory and give results for its finite temperature phase transition. (orig.)