A random matrix model with non-pairwise contracted indices

• Lionni, Luca

• Sasakura, Naoki

Abstract

We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the p-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.

Journal

• Progress of Theoretical and Experimental Physics

  Progress of Theoretical and Experimental Physics 2019 (7), 073A01-, 2019-07

  Oxford University Press (OUP)

Keywords

• A13 Other topics in mathematical physics
• B83 Matrix models
• B86 Statistical methods
• random systems

Details

• CRID: 1050564288359664768
• NII Article ID: 120006708222
• ISSN: 20503911
• DOI: 10.1093/ptep/ptz057
• HANDLE: 2433/243192
• Web Site: http://academic.oup.com/ptep/article-pdf/2019/7/073A01/28914433/ptz057.pdf
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN