Calculation of the Critical Exponent η via RenormalizationGroup Recursion Formulas
Abstract
This paper presents an extension of Wilson's renormalizationgroup calculation of Isingmodel 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 renormalizationgroup 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 ɛ^{2} we obtain η=0.05ɛ^{2}. Numerical results in three dimension are η=0.058, ν=0.588, and γ=1.14. The relation γ=(2η)ν is confirmed.
 Publication:

Physical Review B
 Pub Date:
 July 1973
 DOI:
 10.1103/PhysRevB.8.339
 Bibcode:
 1973PhRvB...8..339G