Restoration of Isotropy in the Ising Model on the Sierpinski Gasket

DOI10.1143/PTP.118.1zbMATH Open1131.82005arXivcond-mat/0603065WikidataQ113079099 ScholiaQ113079099MaRDI QIDQ5436551

Naoto Jajima

Publication date: 17 January 2008

Published in: Progress of Theoretical Physics (Search for Journal in Brave)

Abstract: We study the ferromagnetic Ising model on the Sierpinski gasket (SG), where the spin-spin interactions depends on the direction. Using the renormalization group method, we show that the ratios of the correlation lengths restore the isotropy of the lattice as the temperature approaches zero. This restoration is either partial or perfect, depending on the interactions. In case of partial restoration, we also evaluate the leading-order singular behavior of the correlation lengths.

Full work available at URL: https://arxiv.org/abs/cond-mat/0603065

zbMATH Keywords

renormalization group methodSierpinski gasketferromagnetic Ising modelspin-spin interaction

Mathematics Subject Classification ID

Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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