Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1994-08-30
J.Math.Phys.36:1812-1824,1995
Physics
High Energy Physics
High Energy Physics - Lattice
24 Pages, includes 2 short Mathematica programs appended after "/end" uses phyzzx.tex
Scientific paper
10.1063/1.531087
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the calculation of the high-temperature expansion of the magnetic susceptibility can be performed, at least up to the fourth order, using elementary algebraic manipulations which can be implemented with a computer. These symmetries appear more clearly if we use the 2-adic fractions to label the sites. We then apply the new algebraic methods to the calculation of quantities having a random walk interpretation. In particular, we show that the probability of returning at the starting point after $m$ steps has poles at $D=-2,-4,....-2m$ , where $D$ is a free parameter playing a role similar to the dimensionality in nearest neighbor models.
No associations
LandOfFree
The High-Temperature Expansion of the Hierarchical Ising Model: From Poincaré Symmetry to an Algebraic Algorithm 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 The High-Temperature Expansion of the Hierarchical Ising Model: From Poincaré Symmetry to an Algebraic Algorithm, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The High-Temperature Expansion of the Hierarchical Ising Model: From Poincaré Symmetry to an Algebraic Algorithm will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-51720