1996/12/19 by H. Meyer, Hugues Meyer, J C Anglès d'Auriac +1 · 13 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chiral Potts curve #Computer science #Context (archaeology) #Critical point (mathematics) #Discrete mathematics #Eigenvalues and eigenvectors #Integrable system #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Physics #Potts model #Quantum many-body systems #Quantum mechanics #Random matrix #Spectral line #Statistical mechanics #Statistical physics #Theoretical and Computational Physics #Transfer matrix #Vertex (graph theory) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.55.6608
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 55(6), 6608-6617 (American Physical Society) · 19 pages, RevTex 9 PostScript figures
arxiv created 1996/12/19 · openalex publication_date 1997/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper [H. Meyer, J.-C. Angl`es d'Auriac, and J.-M. Maillard, Phys. Rev. E 55, 5261 (1997)]. We show that the statistical properties of these spectra can serve as a criterion of integrability. It also provides an operational numerical method to locate integrable varieties. In particular, we distinguish the notions of integrability and criticality, considering the two examples of the three-dimensional Ising critical point and the two-dimensional three-state Potts critical point. For complex spectra, which appear frequently in the context of transfer matrices, we show that the notion of independence of eigenvalues for integrable models still holds.