We investigate the critical behavior of three-dimensional ferromagnetic CPN-1 models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical transition in the Heisenberg O(3) universality class, while for N=3 and 4 the system undergoes a first-order transition. For N=3 the transition is very weak and a clear signature of its discontinuous nature is only observed for sizes L 50. We also determine the critical behavior for a large class of lattice Hamiltonians in the large-N limit. The results confirm the existence of a stable large-NCPN-1 fixed point. However, this evidence contradicts the standard picture obtained in the Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter: The presence of a cubic term in the effective LGW field theory for any N≥3 would usually be taken as an indication that these models generically undergo first-order transitions.

Three-dimensional ferromagnetic CPN-1 models / Pelissetto, A.; Vicari, E.. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 100:2(2019). [10.1103/PhysRevE.100.022122]

Three-dimensional ferromagnetic CPN-1 models

Pelissetto A.;
2019

Abstract

We investigate the critical behavior of three-dimensional ferromagnetic CPN-1 models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical transition in the Heisenberg O(3) universality class, while for N=3 and 4 the system undergoes a first-order transition. For N=3 the transition is very weak and a clear signature of its discontinuous nature is only observed for sizes L 50. We also determine the critical behavior for a large class of lattice Hamiltonians in the large-N limit. The results confirm the existence of a stable large-NCPN-1 fixed point. However, this evidence contradicts the standard picture obtained in the Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter: The presence of a cubic term in the effective LGW field theory for any N≥3 would usually be taken as an indication that these models generically undergo first-order transitions.
2019
critical behavior; finite-size scaling; quantum field theory
01 Pubblicazione su rivista::01a Articolo in rivista
Three-dimensional ferromagnetic CPN-1 models / Pelissetto, A.; Vicari, E.. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 100:2(2019). [10.1103/PhysRevE.100.022122]
File allegati a questo prodotto
File Dimensione Formato  
Pelissetto_Three-dimensional_2019.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 768.2 kB
Formato Adobe PDF
768.2 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1343597
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 22
social impact