Two-dimensional super-roughening in the three-dimensional Ising model

We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been carried out to measure the global interfacial width as a functio...

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Published inPhysical review. E Vol. 100; no. 6-1; p. 060101
Main Authors Dashti-Naserabadi, Hor, Saberi, Abbas Ali, Rahbari, S H E, Park, Hyunggyu
Format Journal Article
LanguageEnglish
Published United States 01.12.2019
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Summary:We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been carried out to measure the global interfacial width as a function of temperature for different lattice sizes which is shown to signal the criticality of the model at T_{c} by forming a size-independent cusp in 3D, along with an emergent super-roughening at its 2D cross section. We find that the super-rough state is accompanied by an intrinsic anomalous scaling behavior in the local properties characterized by a set of geometric exponents which are the same as those for a pure 2D Ising model.
ISSN:2470-0053
DOI:10.1103/PhysRevE.100.060101