Complex Gaussian Spin System With Phase Change Problem

The phase transition and critical phenomena study of ferromagnetic systems has always been a very important part in the field of condensed matter physics and statistical physics. In this paper, using the methods of Fourier transformation and moment-space renormalization group et al, we studied the phase transition of several complex Gauss systems, figured out the critical point and critical exponents of the system, simply discussed the critical problem of the system with long rang interactions and the universality of phase transition. The content of this paper includes:1. Using the methods of Fourier transformation and moment-space renormalization group, we studied the critical behaviour of the Gauss model on a two-dimensional triangular lattice, the critical point and the critical exponents are calculated. The result shows that, the critical point of the Gauss model depends not only on the spatial dimension of the system, but also on the coordination number of the site. But the value of the critical exponents depends only on the coordination number. Moreover, Gauss model on such a lattice has the same critical exponent with tetragonal lattices; they belong to the same universal class.2. To the Gauss system on the triangular lattices and hyper-cubic lattices, we called in the long rang interactions. Using the method of Fourier transformation, accurately calculated the critical point of the system under long rang interactions. And at the same time, we discussed the affection of different types of long rang interactions on the critical point; The results show that, under the effect of long rang interactions, the critical temperature of the system increases apparently, comparing with that of only consider the nearest neighbour interactions. Furthermore, the critical behaviour of the system with different kinds of long rang interactions varies greatly.3. Introducing the Gauss model into complex network system, we studied the Gauss model built on the Small World Network, we also figured out the...