Turkish Journal of Physics
Finite qdifferences and the Renormalization Group
DOI

Abstract
We observe that the qdifference operator [1] and its inverse lend themselves naturally to describing systems with discrete dilatation symmetry, in particular, hierarchical lattices [2]. The homogeneity relation satisfied by the singular part of the free energy per bond can be written, D_\lambda f_{\rm sing}(u)=(\ell^d1)f_{\rm sing}(u) /(\lambda 1) where u is the reduced inverse temperature, \lambda=\ell^y, y and d are the temperature critical index and effective dimensionality, respectively; \ell is the rescaling factor. Moreover, we show that the infinite sum which is the solution of this equation is simply given by f_{\rm sing}(u)= u^\psi \left[ {1\over 1\lambda } \int_0^{\lambda u} {g_{\rm rem}(t) \over t^{1+\psi} } D_\lambda t +{1\over 1\lambda^{1}} \int_0^{\lambda^{1} u} {g_{\rm rem}(t) \over t^{1+\psi} } D_{\lambda^{1}} t\right] where g_{\rm rem} has the meaning in [3] and \psi=d/y. This provides a possibly new way to connect the qdifferences to the generalized thermodynamics of Tsallis [4].
First Page
179
Last Page
179
Recommended Citation
ERZAN, Ayşe (1997) "Finite qdifferences and the Renormalization Group," Turkish Journal of Physics: Vol. 21: No. 1, Article 46. Available at: https://journals.tubitak.gov.tr/physics/vol21/iss1/46