Monotonicity of Ursell Functions in the Ising Model

Camia, Federico; Jian, Jiang; Newman, Charles M.

doi:10.1007/s00220-023-04693-x

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction and Main Results1

Proof Of the Main Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the next section, we prove Theorem 1.1. The proof makes use of three key ingredients: the monotonicity of Ursell functions (and thus monotonicity of the first Lee-Yang zero) from [7], bounds on the derivatives of various orders of the free energy from [13] and their consequences (see Theorem 2.5 below), and the analyticity of the free energy for 𝛽 ∈ [0, 𝛽 𝑐 (𝑑)) from [20].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Thermodynamic limit of the first Lee‐Yang zero

Jiang,

Newman

2023

Comm Pure Appl Math

View full text Add to dashboard Cite

We complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in of finite‐volume singularities in . For the Ising model defined on a finite at inverse temperature and external field h, let be the modulus of the first zero (that closest to the origin) of its partition function (in the variable h). We prove that decreases to as Λ increases to where is the radius of the largest disk centered at the origin in which the free energy in the thermodynamic limit is analytic. We also note that is strictly positive if and only if β is strictly less than the critical inverse temperature.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…It is enough to prove the proposition for even 𝑘 since both sides of (2.9) are 0 if 𝑘 is odd. By the signs and mononoticity of Ursell functions (see [25] and Theorem 1 of [7] respectively), we have…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%