The Strong Gauss Lucas Theorem and Analyticity of Correlation Functions via the Lee-Yang Theorem

2021/11/01 by Barry Simon
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Gauss #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Simple (philosophy) #Theoretical and Computational Physics #math-ph #math.CO #math.MP #msc:82B20

paper · pdf · doi:10.1063/5.0077229

arxiv created 2021/11/01 · openalex publication_date 2022/03/01 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We provide a simple mechanism for going from Lee-Yang type theorems to analyticity of correlation functions by exploiting under appreciated inequalities of Newman. We also describe a Lee-Yang approach that recovers the consequences of a low density cluster expansion for spin S models without any combinatorics.

Citations

• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• The (φ4)2 field theory as a classical Ising model