In this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.

Antinucci, G., Giuliani, A., Greenblatt, R.L. (2022). Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit. ANNALES HENRI POINCARE', 23(3), 1061-1139 [10.1007/s00023-021-01107-3].

Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit

Antinucci G.;Giuliani A.;Greenblatt R. L.
2022-01-01

Abstract

In this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.
2022
Antinucci, G., Giuliani, A., Greenblatt, R.L. (2022). Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit. ANNALES HENRI POINCARE', 23(3), 1061-1139 [10.1007/s00023-021-01107-3].
File in questo prodotto:
File Dimensione Formato  
Antinucci2022_Article_Non-integrableIsingModelsInCyl.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 1.29 MB
Formato Adobe PDF
1.29 MB Adobe PDF Visualizza/Apri

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/11590/404623
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact