Physicists have been trying to create artificial magnetic systems using ultra-cold atomic gases as their simulators. However, behavior of many ultra-cold atomic systems is not very well understood yet. Ultra-cold fermionic alkaline earth atomic (AEA) gases are one of those systems. In this thesis, we study the effects of thermal fluctuations on the overall macroscopic behavior of ultra-cold fermionic AEA gases using a particular semiclassical model. We study the AEA systems on a square lattice with periodic boundary conditions. To investigate the behavior of AEA systems under the effects of thermal fluctuations, we analyze several different types of correlation functions, which correspond to different physical observables. We analyze the correlation functions using the results obtained from Monte Carlo simulations. We show that for the cases studied, all the correlation functions approach zero as the system size goes to infinity at any temperature, indicating that no phase transition occurs as a consequence of thermal fluctuations
