The mean-field quantum Heisenberg ferromagnet via representation theory

Gil Alon; Gady Kozma

doi:10.1214/20-AIHP1067

The mean-field quantum Heisenberg ferromagnet via representation theory

Gil Alon, Gady Kozma

Mathematics

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

Abstract

We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function α_k2^α1+···+^αn where α_k is the number of cycles of length k of a permutation. In the mean-field case, we simplify the formula further, arriving at a closed-form expression for the magnetisation, which allows to analyse the phase transition.

Original language	English
Pages (from-to)	1203-1228
Number of pages	26
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1214/20-AIHP1067
State	Published - Aug 2021

Bibliographical note

Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2021.

Keywords

Interchange process
Magnetisation
Phase transition
Quantum heizenberg ferromagnet
Random walk
Symmetric group

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10.1214/20-AIHP1067

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abstract = "We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function αk2α1+···+αn where αk is the number of cycles of length k of a permutation. In the mean-field case, we simplify the formula further, arriving at a closed-form expression for the magnetisation, which allows to analyse the phase transition.",

keywords = "Interchange process, Magnetisation, Phase transition, Quantum heizenberg ferromagnet, Random walk, Symmetric group",

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AU - Kozma, Gady

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N2 - We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function αk2α1+···+αn where αk is the number of cycles of length k of a permutation. In the mean-field case, we simplify the formula further, arriving at a closed-form expression for the magnetisation, which allows to analyse the phase transition.

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KW - Interchange process

KW - Magnetisation

KW - Phase transition

KW - Quantum heizenberg ferromagnet

KW - Random walk

KW - Symmetric group

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

The mean-field quantum Heisenberg ferromagnet via representation theory

Abstract

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Keywords

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