Mosaic Square Lattice Gaussian Model And The One Dimensional Antiferromagnetic Phase Transition Theory Of The Gaussian Model

Phase transitions and critical phenomena are quite important study field in statistical physics. As is well known to us, the conversion of iron from paramagnetic to ferromagnetic form, the transitions from conductor to superconductor and from normal fluid to superfluid are examples of critical phenomena. In this thesis we study the regular square-lattice Gaussian model and antiferromagnetics Gaussian model by real space renormalization group transformation.The main contents of this thesis are as follows:1. Using the equivalent transformation and spin-rescaling methods, the Gaussian model on a square decorated lattice is studied. It is found that this model can be transformed into the regular square-lattice Gaussian model in the case of considering the nearest-neighbor and next-nearest-neighbor interactions. By calculating the regular square-lattice Gaussian model, we get the exact phase diagram of the decorated square lattices.2. The one-dimensional antiferromagnetics Gaussian model with nearby interaction is calculated by methods of the strict solution and coordinate space renormalization group. The first method is to get the free energy function by calculating the partition function directly. Then we analyse the phase transition of antiferromagnetics Gaussian model by the partition function's irregularity. The antiferromagnetics Gaussian model by renormalization group method is studied. It is found that the same results can be obtained with both methods.