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Journal of Superconductivity and Novel Magnetism

Real Space Renormalization Group Investigation of the Mixed Spins S = 1/2 and S = 3/2 Model

M. Bourass, Abdellah Zradba, S. Zouhair, A. El Antari, M. El Bouziani, M. Madani, A. Alrajhi

Published Jul 14, 2017• 16 citations
Publisher
DOI
10.1007/s10948-017-4242-y

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Faithfulness of Real-Space Renormalization Group Maps

Katsuya O. Akamatsu, Naoki Kawashima

Abstract The behavior of $$b=2$$ b = 2 real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical $$q=2,3,4$$ q = 2 , 3 , 4 Potts spin configurations. While the majority rule is generally believed to work well, a more thorough investigation of the action of the map has yet to be considered in the literature. When fixing the size of the renormalized lattice $$L_g$$ L g and allowing the source configuration size $$L_0$$ L 0 to vary, we observed that the RG flow of the spin and energy correlation under the majority rule map appear to converge to a nontrivial model-dependent curve. We denote this property as “faithfulness”, because it implies that some information remains preserved by RSRG maps that fall under this class. Furthermore, we show that $$b=2$$ b = 2 weighted majority-like RSRG maps acting on the $$q=2$$ q = 2 Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule.

arXiv:2403.14955•Journal of Statistical Physics•Aug 27, 2024•0 citations
Abstract The behavior of b=2b=2b=2 b = 2 real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical q=2,3,4q=2,3,4q=2,3,4 q = 2 , 3 , 4 Potts spin configurations. While the majority rule is generally believed to work well, a more thorough investigation of the action of the map has yet to be considered in the literature. When fixing the size of the renormalized lattice LgL_gLg​ L g and allowing the source configuration size L0L_0L0​ L 0 to vary, we observed that the RG flow of the spin and energy correlation under the majority rule map appear to converge to a nontrivial model-dependent curve. We denote this property as “faithfulness”, because it implies that some information remains preserved by RSRG maps that fall under this class. Furthermore, we show that b=2b=2b=2 b = 2 weighted majority-like RSRG maps acting on the q=2q=2q=2 q = 2 Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule.