Renormalization Group Transformations Near the Critical Point: Some Rigorous Results

Details Renormalization Group Transformations Near the Critical Point: Some Rigorous Results Renormalization Group Transformations Near the Critical Point: Some Rigorous Results

2011-08-16

arxiv.org/abs/1108.3308v2

J. Math. Phys. 52: 113507 (2011)

Physics

Mathematical Physics

13 pages

Scientific paper

We consider renormalization group (RG) transformations for classical Ising-type lattice spin systems in the infinite volume limit. Formally, the RG maps a Hamiltonian H into a renormalized Hamiltonian H': exp(-H'(\sigma'))=\sum_\sigma T(\sigma, \sigma')exp(-H(\sigma)), where T(\sigma, \sigma') denotes a specific RG probability kernel, \sum_\sigma' T(\sigma, \sigma')=1, for every configuration \sigma. With the help of the Dobrushin uniqueness condition and standard results on the polymer expansion, Haller and Kennedy gave a sufficient condition for the existence of the renormalized Hamiltonian in a neighborhood of the critical point. By a more complicated but reasonably straightforward application of the cluster expansion machinery, the present investigation shows that their condition would further imply a band structure on the matrix of partial derivatives of the renormalized interaction with respect to the original interaction. This in turn gives an upper bound for the RG linearization.

Affiliated with

Also associated with

No associations

Rating

Renormalization Group Transformations Near the Critical Point: Some Rigorous Results does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Renormalization Group Transformations Near the Critical Point: Some Rigorous Results, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalization Group Transformations Near the Critical Point: Some Rigorous Results will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-196446