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

نتاج البحث: نشر في مجلة › مقالة › مراجعة النظراء

ملخص

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.

اللغة الأصلية	الإنجليزيّة
الصفحات (من إلى)	1203-1228
عدد الصفحات	26
دورية	Annales de l'institut Henri Poincare (B) Probability and Statistics
مستوى الصوت	57
رقم الإصدار	3
المعرِّفات الرقمية للأشياء	https://doi.org/10.1214/20-AIHP1067
حالة النشر	نُشِر - أغسطس 2021

ملاحظة ببليوغرافية

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

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10.1214/20-AIHP1067

الملفات والروابط الأخرى

Link to publication in Scopus

قم بذكر هذا

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title = "The mean-field quantum Heisenberg ferromagnet via representation theory",

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.",

year = "2021",

month = aug,

doi = "10.1214/20-AIHP1067",

language = "אנגלית",

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T1 - The mean-field quantum Heisenberg ferromagnet via representation theory

AU - Alon, Gil

AU - Kozma, Gady

N1 - Publisher Copyright: © Association des Publications de l’Institut Henri Poincaré, 2021.

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.

AB - 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.

KW - Interchange process

KW - Magnetisation

KW - Phase transition

KW - Quantum heizenberg ferromagnet

KW - Random walk

KW - Symmetric group

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U2 - 10.1214/20-AIHP1067

DO - 10.1214/20-AIHP1067

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AN - SCOPUS:85111978886

SN - 0246-0203

VL - 57

SP - 1203

EP - 1228

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

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

IS - 3

ER -

The mean-field quantum Heisenberg ferromagnet via representation theory

ملخص

ملاحظة ببليوغرافية

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الملفات والروابط الأخرى

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