Minimalistic real-space Renormalization of 4x4 Ising and Potts Models in two dimensions
File(s)
Published version
Author(s)
Willis, G
Pruessner, G
Keelan, J
Type
Journal Article
Abstract
We introduce and discuss a real-space renormalization group (RSRG) procedure on very
small lattices, which in principle does not require any of the usual approximations, e.g., a
cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried
out numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Model
and the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of the
correlation length exponent and the magnetization exponent are typically within 3–7% of
the exact values. The 4-state Potts Model generates a third magnetic exponent, which
seems to be unknown in the literature. A number of questions about the meaning of
certain exponents and the procedure itself arise from its use of symmetry principles and
its application to the q = 5 Potts Model.
small lattices, which in principle does not require any of the usual approximations, e.g., a
cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried
out numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Model
and the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of the
correlation length exponent and the magnetization exponent are typically within 3–7% of
the exact values. The 4-state Potts Model generates a third magnetic exponent, which
seems to be unknown in the literature. A number of questions about the meaning of
certain exponents and the procedure itself arise from its use of symmetry principles and
its application to the q = 5 Potts Model.
Date Issued
2015-06-23
Date Acceptance
2015-06-08
Citation
Frontiers in Physics, 2015, 3
ISSN
2296-424X
Publisher
Frontiers
Journal / Book Title
Frontiers in Physics
Volume
3
Copyright Statement
© 2015 The Authors. This Document is Protected by copyright and was first published by Frontiers. All rights reserved. it is reproduced with permission
License URL
Publication Status
Published
Article Number
46