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Condensed Matter > Statistical Mechanics
Title: Faithfulness of Real-Space Renormalization Group Maps
(Submitted on 22 Mar 2024)
Abstract: The behavior of $b=2$ real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical $q=2,3,4$ 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 $L_g$ and allowing the source configuration size $L_0$ 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 $b=2$ weighted majority-like RSRG maps acting on the $q=2$ Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule.
Submission history
From: Katsuya Akamatsu [view email][v1] Fri, 22 Mar 2024 05:18:46 GMT (1224kb,D)
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