The relation between ferromagnets, Phi4 and non-linear sigma model

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SUMMARY

The discussion centers on the relationship between phi4 theory, the non-linear sigma model, and ferromagnets, specifically referencing the paper "Phys.Rev.B14(1976)3110." It establishes that phi4 theory serves as a coarse-grained approach to describe the long-distance behavior of Heisenberg ferromagnets, providing superior results compared to mean-field theory. The non-linear sigma model is identified as a low-temperature expansion of ferromagnets, illustrating different methodologies to analyze magnetic systems. The confusion arises from the interpretation of phi4 theory as an expansion around mean-field theory.

PREREQUISITES
  • Understanding of phi4 field theory
  • Familiarity with non-linear sigma models
  • Knowledge of Heisenberg ferromagnets
  • Concept of mean-field theory in statistical mechanics
NEXT STEPS
  • Study the derivation of phi4 theory in the context of ferromagnetism
  • Explore the mathematical framework of non-linear sigma models
  • Investigate the implications of low-temperature expansions in statistical mechanics
  • Review the historical context and advancements in mean-field theory
USEFUL FOR

Physicists, particularly those specializing in condensed matter physics, theoretical physicists, and researchers interested in the mathematical modeling of magnetic systems.

Aethermimicus
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TL;DR
It is possible to describe the long-distance behavior of the Heisenberg ferromagnets in two different ways:the phi4 theory which corresponds to an expansion around mean-field thoery and the nonlinear sigma model obtained by low-temperature expansion.
I'm struggling to understand the relation between phi4 theory,non-linear sigma model and ferromagnets.
I've read this in a paper(Phys.Rev.B14(1976)3110):'It is possible to describe the long-distance behavior of the Heisenberg ferromagnets in two different ways:the phi4 theory which corresponds to an expansion around mean-field thoery and the nonlinear sigma model obtained by low-temperature expansion.'
I do understand that phi4 field theory is a coarse graining version of ferromagnets (for example,the Ising model),and achieve better results than mean field theory,but why is it 'an expansion around mean field theory'?
Also I fail to understand non-linear sigma model as a low-temperature exapansion of ferromagnets.
 

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