Renormalization group equations and the gaussian spin model

P. Coullet, E. Tirapegui

Thomas L. Bell, Kenneth Geddes Wilson

Accurate calculations of the thermodynamic properties of a system near its critical point are now possible using finite-lattice approximations to renormalization groups. In order to investigate some features of such approximations, we introduce a linear-renormalization-group transformation appropriate to a system of continuous spins like the Gaussian model of Berlin and Kac. We solve the renormalization-group equations for the Gaussian model exactly, and then study in detail a finite-lattice approximation to the renormalization group for the three-dimensional case. The renormalization-group transformation contains a parameter $b$. The exact transformation has fixed points only for $b={2}^{\ensuremath{-}\frac{5}{2}}$. The approximate transformation has fixed points for a range of values of $b$ around ${2}^{\ensuremath{-}\frac{5}{2}}$. Eigenvalues of the transformation, which determine critical exponents, depend on the value of $b$ used in the calculation. We study the problem of identifying the correct value of $b$.

U. Köbler, A. Hoser

Ye Fei, Guo-Hui Ding, Xu Bo-wei

We utilize the renormalization group (RG) technique to analyze the Ising critical behavior in the double frequency sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Ising critical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well.

YEFei, DINGGuo-Hui, Guohui +2 more

We utilize the renormallzation group (RG) technique to analyze the Ising critical behavior in the double frequency Sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Ising critical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well.