Fisher's zeros in lattice gauge theory

Abstract

In this thesis, we study the Fisher's zeros in lattice gauge theory. The analysis of singularities in the complex coupling plane is an important tool to understand the critical phenomena of statistical models. The Fisher's zero structure characterizes the scaling properties of the underlying models [40, 33] and has a strong influence on the complex renormalization group transformation flows in the region away from both the strong and weak coupling regimes [24].

Study of phase transitions in spin and gauge models using Fisher's zeros

“…When we reweight data away from the value of β that it was created at we need to know what the range is that the observables are still valid in. It was shown by Daping Du [14] that the radius of confidence, the distance we can move from the value of β the simulation was taken at in the complex plane, for a semi-Gaussian distribution can be written as:…”

“…All of these models will be on symmetric lattices. The method that we will be using is the density of state which at infinite volume is equivalent to the entropy of the system, and has been studied at length by us in [14,10,3,12] as a reliable method of finding the Fisher's zeros. This method is discussed in much more detail in chapter 2 and the computer program to generate the density of state can be found in B.1.…”