Calculation of the Critical Exponent η via Renormalization-Group Recursion Formulas
Abstract
This paper presents an extension of Wilson's renormalization-group calculation of Ising-model critical exponents to include calculation of the critical exponent η. New recursion formulas are derived using the simplest set of consistent approximations which allow a nonzero η. They are intended to demonstrate, qualitatively, how nonzero values for η are consistent with the renormalization-group approach; they do not represent systematic, quantitative improvements to Wilson's earlier calculation of the exponents ν and γ. The equations are solved both by ɛ expansion about four dimensions and by numerical integration in three dimensions. To order ɛ2 we obtain η=0.05ɛ2. Numerical results in three dimension are η=0.058, ν=0.588, and γ=1.14. The relation γ=(2-η)ν is confirmed.
- Publication:
-
Physical Review B
- Pub Date:
- July 1973
- DOI:
- 10.1103/PhysRevB.8.339
- Bibcode:
- 1973PhRvB...8..339G