Polynomial degeneracy for the first m energy levels of the antiferromagnetic Ising model

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dc.contributor.authorJiménez, Andrea
dc.date.accessioned2022-11-30T02:46:27Z
dc.date.available2022-11-30T02:46:27Z
dc.date.issued2021
dc.description.abstractIn this work, we continue our investigation on the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. On the one hand, according to R. Moessner and A. P. Ramirez [11], the antiferromagnetic Ising model on triangulations exhibits geometrical frustration, a well-studied concept in condensed matter physics. Typical geometrically frustrated systems present an exponential ground state degeneracy. On the other hand, the dual graph of a triangulation of a closed Riemann surface is a cubic graph. Cubic bridgeless graphs have exponentially many perfect matchings [3, 5], which implies in the case of planar triangulations, an exponential ground state degeneracy. However, this phenomenon does not persist for triangulations of higher genus surfaces. A possible explanation for a geometrically frustrated system with a low ground state degeneracy is that exponentially many states exist at a low energy level. In this work, we constructively show that this explanation does not match with the behavior of all triangulations of closed Riemann surfaces. To be more specific, for each integer m \geq 1m≥1, we construct a collection of triangulations \{T_n\}_{n > N(m)}{Tn} n>N(m) of a fixed closed Riemann surface with the property that the degeneracy of each of the first mm energy levels of T_nTn is a polynomial in the order nn of T_nTn.en_ES
dc.facultadFacultad de Ingenieríaen_ES
dc.file.nameJimenez_Pol2021.pdf
dc.identifier.citationAndrea Jiménez, Polynomial degeneracy for the first mm energy levels of the antiferromagnetic Ising model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), no. 2, pp. 201–212en_ES
dc.identifier.doi10.4171/AIHPD/101
dc.identifier.urihttp://repositoriobibliotecas.uv.cl/handle/uvscl/7377
dc.languageen
dc.publisherEuropean Mathematical Society
dc.sourceAnnales de l’Institut Henri Poincaré D
dc.subjectANTIFERROMAGNETIC ISING MODELen_ES
dc.subjectTRIANGULATIONSen_ES
dc.subjectGROUND STATE DEGENERACYen_ES
dc.subjectGEOMETRICAL FRUSTRATIONen_ES
dc.subjectLOW ENERGY LEVEL.en_ES
dc.titlePolynomial degeneracy for the first m energy levels of the antiferromagnetic Ising model
dc.typeArticulo
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