Dualities for Ising Networks
Journal
Physical Review Letters
Journal Volume
121
Journal Issue
25
Date Issued
2018
Author(s)
Abstract
In this Letter, we study the equivalence between planar Ising networks and cells in the positive orthogonal Grassmannian. We present a microscopic construction based on amalgamation, which establishes the correspondence for any planar Ising network. The equivalence allows us to introduce two recursive methods for computing correlators of Ising networks. The first is based on duality moves, which generate networks belonging to the same cell in the Grassmannian. This leads to fractal lattices where the recursion formulas become the exact renormalization group equations of the effective couplings. The second, we use an amalgamation in which each iteration doubles the size of the seed lattice. This leads to an efficient way of computing the correlator where the complexity scales logarithmically with respect to the number of spin sites. © 2018 authors. Published by the American Physical Society.
Other Subjects
Correlators; Metals; Statistical mechanics; Effective coupling; Fractal lattices; Grassmannian; Recursion formulas; Recursive methods; Renormalization group equations; Iterative methods
Type
journal article