Mean-field theory for quantum spin chains
Abstract
Mean-field theory is a widely used approximation for describing phase transitions, particularly effective above the upper critical dimension. Its origins can be traced back to the van der Waals theory of the liquid-gas transition and Weiss's molecular field theory of the paramagnetic-ferromagnetic transition. However, it was Lev D. Landau who provided a unifying and general framework applicable to a broad class of physical systems. The mean-field approach typically involves neglecting thermal fluctuations, which is a reasonable assumption in many classical contexts. However, its application to quantum phase transitions at zero temperature is less common. The aim of this short pedagogical paper is to explore and clarify the use of the mean-field approach in the less familiar domain of quantum phase transitions. We specifically consider the Ising model and the Blume-Capel model.
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BibTeX
@misc{martirosyan2026meanfield,
title = {{Mean-field theory for quantum spin chains}},
author = {Mylène Martirosyan and Astrid Monin-Baroille and Leïla Moueddene and Mohammed M. Shabat and Bertrand Berche},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04717},
eprint = {2609.04717},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04717},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mean-field theory for quantum spin chains
AU - Mylène Martirosyan
AU - Astrid Monin-Baroille
AU - Leïla Moueddene
AU - Mohammed M. Shabat
AU - Bertrand Berche
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04717
UR - https://arxiv.org/abs/2609.04717
AB - Mean-field theory is a widely used approximation for describing phase transitions, particularly effective above the upper critical dimension. Its origins can be traced back to the van der Waals theory of the liquid-gas transition and Weiss's molecular field theory of the paramagnetic-ferromagnetic transition. However, it was Lev D. Landau who provided a unifying and general framework applicable to a broad class of physical systems. The mean-field approach typically involves neglecting thermal fluctuations, which is a reasonable assumption in many classical contexts. However, its application to quantum phase transitions at zero temperature is less common. The aim of this short pedagogical paper is to explore and clarify the use of the mean-field approach in the less familiar domain of quantum phase transitions. We specifically consider the Ising model and the Blume-Capel model.
ER -