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

מתמטיקה

פרסום מחקרי: פרסום בכתב עת › מאמר › ביקורת עמיתים

תקציר

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.

שפה מקורית	אנגלית
עמודים (מ-עד)	1203-1228
מספר עמודים	26
כתב עת	Annales de l'institut Henri Poincare (B) Probability and Statistics
כרך	57
מספר גיליון	3
מזהי עצם דיגיטלי (DOIs)	https://doi.org/10.1214/20-AIHP1067
סטטוס פרסום	פורסם - אוג׳ 2021

הערה ביבליוגרפית

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

גישה למסמך

10.1214/20-AIHP1067

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Link to publication in Scopus

פורמט ציטוט ביבליוגרפי

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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",

author = "Gil Alon and Gady Kozma",

note = "Publisher Copyright: {\textcopyright} Association des Publications de l{\textquoteright}Institut Henri Poincar{\'e}, 2021.",

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doi = "10.1214/20-AIHP1067",

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AU - Kozma, Gady

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PY - 2021/8

Y1 - 2021/8

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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The mean-field quantum Heisenberg ferromagnet via representation theory

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