We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry Sq. After sending to zero the number of replicas they correspond to the renormalization group fixed points of the q-state Potts model with quenched disorder. We find that all solutions with non-zero disorder possess q-independent sectors, pointing to superuniversality (i.e. symmetry independence) of some critical exponents. The solution corresponding to the random bond ferromagnet, for which disorder vanishes as q→2, allows for superuniversality of the correlation length exponent ν [PRL 118 (2017) 250601]. Of the two solutions which are strongly disordered for all values of q, one is completely q-independent and accounts for the zero-temperature percolation fixed point of the randomly bond diluted ferromagnet. The other is the main candidate to describe the Nishimori-like fixed point of the Potts model with ±J disorder, and leaves room for superuniversality of the magnetic exponent η, a possibility not yet excluded by available numerical data.

On superuniversality in the q-state Potts model with quenched disorder / Delfino, Gesualdo; Tartaglia, Elena. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2017:12(2017), pp. 1-19. [10.1088/1742-5468/aa9bad]

On superuniversality in the q-state Potts model with quenched disorder

Delfino, Gesualdo;
2017

Abstract

We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry Sq. After sending to zero the number of replicas they correspond to the renormalization group fixed points of the q-state Potts model with quenched disorder. We find that all solutions with non-zero disorder possess q-independent sectors, pointing to superuniversality (i.e. symmetry independence) of some critical exponents. The solution corresponding to the random bond ferromagnet, for which disorder vanishes as q→2, allows for superuniversality of the correlation length exponent ν [PRL 118 (2017) 250601]. Of the two solutions which are strongly disordered for all values of q, one is completely q-independent and accounts for the zero-temperature percolation fixed point of the randomly bond diluted ferromagnet. The other is the main candidate to describe the Nishimori-like fixed point of the Potts model with ±J disorder, and leaves room for superuniversality of the magnetic exponent η, a possibility not yet excluded by available numerical data.
2017
12
1
19
123303
http://iopscience.iop.org/article/10.1088/1742-5468/aa9bad/pdf
https://arxiv.org/abs/1709.00364
Delfino, Gesualdo; Tartaglia, Elena
File in questo prodotto:
File Dimensione Formato  
17_DT_potts_random.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 1.18 MB
Formato Adobe PDF
1.18 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/20.500.11767/67596
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
social impact