Monotonicity of Ursell Functions in the Ising Model

Federico Camia; Jianping Jiang; Charles Newman

doi:10.1007/s00220-023-04693-x

Monotonicity of Ursell Functions in the Ising Model

Federico Camia, Jianping Jiang, Charles Newman

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions u₂_k satisfy: (- 1) ^k^-¹u₂_k is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field h: its closest zero to the origin (in the variable h) moves towards the origin as an arbitrary interaction increases.

Original language	English (US)
Journal	Communications In Mathematical Physics
DOIs	https://doi.org/10.1007/s00220-023-04693-x
State	Accepted/In press - 2023

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s00220-023-04693-x

Cite this

@article{d32236b4b6f54a6cbd0cc25b050df07c,

title = "Monotonicity of Ursell Functions in the Ising Model",

abstract = "In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions u2k satisfy: (- 1) k-1u2k is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field h: its closest zero to the origin (in the variable h) moves towards the origin as an arbitrary interaction increases.",

author = "Federico Camia and Jianping Jiang and Charles Newman",

note = "Funding Information: The research of the second author was partially supported by NSFC grants 11901394 and 12271284. The authors thank Qi Hou for a critical reading of an earlier draft and Senya Shlosman for useful communications. The authors also thank the reviewers for many useful comments and suggestions. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

doi = "10.1007/s00220-023-04693-x",

language = "English (US)",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

}

TY - JOUR

T1 - Monotonicity of Ursell Functions in the Ising Model

AU - Camia, Federico

AU - Jiang, Jianping

AU - Newman, Charles

N1 - Funding Information: The research of the second author was partially supported by NSFC grants 11901394 and 12271284. The authors thank Qi Hou for a critical reading of an earlier draft and Senya Shlosman for useful communications. The authors also thank the reviewers for many useful comments and suggestions. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions u2k satisfy: (- 1) k-1u2k is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field h: its closest zero to the origin (in the variable h) moves towards the origin as an arbitrary interaction increases.

AB - In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions u2k satisfy: (- 1) k-1u2k is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field h: its closest zero to the origin (in the variable h) moves towards the origin as an arbitrary interaction increases.

UR - http://www.scopus.com/inward/record.url?scp=85151441720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85151441720&partnerID=8YFLogxK

U2 - 10.1007/s00220-023-04693-x

DO - 10.1007/s00220-023-04693-x

M3 - Article

AN - SCOPUS:85151441720

SN - 0010-3616

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -

Monotonicity of Ursell Functions in the Ising Model

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this