Lee–Yang Property and Gaussian Multiplicative Chaos

Charles M. Newman; Wei Wu

doi:10.1007/s00220-019-03453-0

Lee–Yang Property and Gaussian Multiplicative Chaos

Charles M. Newman, Wei Wu

Mathematics

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

Abstract

The Lee–Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee–Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee–Yang property to distribution tail behavior.

Original language	English (US)
Pages (from-to)	153-170
Number of pages	18
Journal	Communications In Mathematical Physics
Volume	369
Issue number	1
DOIs	https://doi.org/10.1007/s00220-019-03453-0
State	Published - Jul 1 2019

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Lee–Yang Property and Gaussian Multiplicative Chaos",

abstract = "The Lee–Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee–Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee–Yang property to distribution tail behavior.",

author = "Newman, {Charles M.} and Wei Wu",

note = "Funding Information: Acknowledgements. The research reported here was supported in part by U.S. NSF Grant DMS-1507019. We thank P.-F. Rodriguez, T. Spencer and a very conscientious anonymous referee for useful communications and suggestions. Publisher Copyright: {\textcopyright} 2019, The Author(s).",

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N1 - Funding Information: Acknowledgements. The research reported here was supported in part by U.S. NSF Grant DMS-1507019. We thank P.-F. Rodriguez, T. Spencer and a very conscientious anonymous referee for useful communications and suggestions. Publisher Copyright: © 2019, The Author(s).

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N2 - The Lee–Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee–Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee–Yang property to distribution tail behavior.

AB - The Lee–Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee–Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee–Yang property to distribution tail behavior.

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Lee–Yang Property and Gaussian Multiplicative Chaos

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