Monte Carlo study of a generalized icosahedral model on the simple cubic lattice

• Verfasst von: Hasenbusch, Martin [VerfasserIn]
• Titel: Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Verf.angabe: Martin Hasenbusch
• E-Jahr: 2020
• Jahr: 6 July 2020
• Umfang: 16 S.
• Fussnoten: Gesehen am 23.07.2020
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2020
• Band/Heft Quelle: 102(2020,2) Artikel-Nummer 024406, 16 Seiten
• ISSN Quelle: 2469-9969
• DOI: doi:10.1103/PhysRevB.102.024406
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: critical exponents
• Sach-SW: renormalization-group
• K10plus-PPN: 1725398451

Abstract

We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take 1 of 12 vectors of unit length which are given by the normalized vertices of the icosahedron as value. Similar to the Blume-Capel model, where in addition to -1 and 1, as in the Ising model, the spin might take the value 0, we add in the generalized model (0,0,0) as allowed value. There is a parameter D that controls the density of these voids. For a certain range of D, the model undergoes a second-order phase transition. On the critical line, O(3) symmetry emerges. Furthermore, we demonstrate that within this range, similar to the Blume-Capel model on the simple cubic lattice, there is a value of D, where leading corrections to scaling vanish. We perform Monte Carlo simulations for lattices of a linear size up to L = 400 by using a hybrid of local Metropolis and cluster updates. The motivation to study this particular model is mainly of technical nature. Less memory and CPU time are needed than for a model with O(3) symmetry at the microscopic level. As the result of a finite-size scaling analysis we obtain nu = 0.711 64(10), eta = 0.037 84(5), and omega = 0.759( 2) for the critical exponents of the three-dimensional Heisenberg universality class. The estimate of the irrelevant renormalization group eigenvalue that is related with the breaking the O(3) symmetry is y(ico) = -2.19(2).