Browsing by Subject "Quantum Field Theory"

In QCD there exists a low-temperature color confining disordered phase and a high-temparature color non-confining ordered phase. In the color non-confining ordered phase we can measure the order of the system to be one of the three centers of $\SU(3)$. We naturally measure the pure gauge field to be ordered to one of the centers. Yet, it is of interest to consider systems that exist in two different phases at once. These two-phase systems have been hypothesized to hold relevance to the cosmological quark-hadron phase transition. In this thesis for pure $\SU(N)$ gauge theory we generalize a method to produce a system that possesses two different ordered phases at once. Between these two ordered phases there naturally lies an interface which we call the order-order (o-o) interface. The interface is formed with a twist in the lattice. This twist creates a discontinuity in the measured Polyakov loop ordering which indicates the existence of an interface. In the literature the measurement of the unique o-o interface tension of QCD has been performed. In this work we inspect the formation of such interfaces in pure $\SU(4)$ gauge theory. For $\SU(4)$ there exists two possible interfaces. We measure the ratio of the surface tension of the two possible interfaces $\alpha_{z_2}/\alpha_{z_1}$, and compare the results to literature findings. At $T=1.2T_c$ we measure this ratio to be $\alpha_{z_2}/\alpha_{z_1} \approx 1.291 \pm 0.0050$. It has also been predicted that at high inverse coupling this ratio approaches Casimir scaling $\sigma_2/\sigma_1=4/3$. Our results are suggestive of this behavior. Additionally, we inspect the continuum limit scaling of the measured interface tension and the functions necessary to produce the interface tension. We find that the function which is integrated to measure the interface tensions approaches a Dirac delta function. Lastly we discuss the errors of our sample data. Our findings show that for $\SU(4)$ the two possible interfaces undergo critical freezing in the phase transition regions.