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

Fecha

2021

Profesor Guía

Formato del documento

Articulo

ORCID Autor

Título de la revista

ISSN de la revista

Título del volumen

Editor

European Mathematical Society

ISBN

ISSN

item.page.issne

item.page.doiurl

Departamento o Escuela

Determinador

Recolector

Especie

Nota general

Resumen

In 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.

Descripción

Lugar de Publicación

Auspiciador

Palabras clave

ANTIFERROMAGNETIC ISING MODEL, TRIANGULATIONS, GROUND STATE DEGENERACY, GEOMETRICAL FRUSTRATION, LOW ENERGY LEVEL.

Licencia

URL Licencia