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:2403.14955Journal of Statistical PhysicsAug 27, 20240 citations

Institute of Physics eBooks

Real space renormalization group

M. A. Contínentino

Published Apr 1, 2021• 12 citations

Publisher

DOI: 10.1088/978-0-7503-3395-5ch5

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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.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:2403.14955Journal of Statistical PhysicsAug 27, 20240 citations

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.