Approximate Renormalization Group Calculations of Cubic Crossover.
Abstract
The effect of a small cubic anisotropic interaction near the critical point of an isotropic spin system is analyzed with the use of a variational renormalization group approximation. The transformation used is the one hypercube lower bound recursion. The equations for the isotropic fixed point and the anisotropic eigenperturbation were put in the form of one dimensional integral equations and were generalized for noninteger spin dimensionality n. These equations were then solved numerically for three space dimensions and as a byproduct of this calculation, the critical index nu for the isotropic system is determined in the region d = 3 and 1 less than n less than 4. The values obtained for this exponent are in very good agreement with high temperature series results.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1977
 Bibcode:
 1977PhDT........13Y
 Keywords:

 Physics: Condensed Matter;
 Anisotropy;
 Approximation;
 Cubic Lattices;
 Isotropic Media;
 Critical Point;
 Group Theory;
 Integral Equations;
 SpinLattice Relaxation;
 SolidState Physics