Abstract
The critical limit principle of maximum entropy is put forward, it’s a sufficient condition to obtain accurate critical points, and ensure that the new phase system is still in the maximum entropy state. Two representations for the phase transition of Ising models are found; the universal formula of critical points is explained by thermodynamics. From the point of view of fractal geometry and the correspondence between symmetry and conservation, the scaling laws are reinterpreted. The self consistence equations for the universal class are set up, by which and the scaling laws higher accurate exponents to date are obtained. The temperature where the self similar transformation disappears is calculated.
Highlights
As a fundamental issue, the critical phenomena theory has pervaded modern physics, the approach to the critical point, the critical fluctuation, and the critical exponents help us understand critical laws deeply
The precise calculation of critical points and critical exponents is the common goal of the researchers
The symmetry analysis that is usually applied in particle physics makes our research to a new state, and has got more quantitative results [1]
Summary
The critical phenomena theory has pervaded modern physics, the approach to the critical point, the critical fluctuation, and the critical exponents help us understand critical laws deeply. According to the fractal theory that a system containing a large plenty of lattice spins becomes ordered as the same as a point spin is a kind of spin contraction mapping, which ensures the uniqueness and existence of self similar transformation [3]. This principle pledges the uniqueness of the critical point. There is a unique finite side length n* at the critical point for any one system, which accords with the result of numerical calculation [2]
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