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Related Experiment Videos

Inverse Mermin-Wagner theorem for classical spin models on graphs.

R Burioni1, D Cassi, A Vezzani

  • 1Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica, Università di Parma, Parco Area delle Scienze n. 7A, 43100 Parma, Italy. burioni@pr.infn.it

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

Researchers proved spontaneous magnetization in finite temperature classical spin models on specific graphs. This finding inverts the Mermin-Wagner theorem, offering a general condition for symmetry breaking on inhomogeneous structures.

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Area of Science:

  • Statistical Mechanics
  • Graph Theory
  • Condensed Matter Physics

Background:

  • The Mermin-Wagner theorem typically prohibits spontaneous magnetization in systems with continuous symmetry on low-dimensional lattices.
  • Understanding symmetry breaking in complex, inhomogeneous structures remains a key challenge in statistical physics.

Purpose of the Study:

  • To invert the Mermin-Wagner theorem by demonstrating spontaneous magnetization under specific graph conditions.
  • To establish a general condition for spontaneous symmetry breaking in classical spin models on graphs.

Main Methods:

  • Analysis of classical spin models with O(n) symmetry on transient on the average graphs.
  • Utilizing concepts of random walks and their return probabilities (F<1) on graphs.

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Main Results:

  • Proven existence of spontaneous magnetization at finite temperatures for classical spin models on transient on the average graphs.
  • Demonstrated that a return probability F<1 is a sufficient condition for spontaneous symmetry breaking.
  • Extended the result to include the Ising model (n=1) as a special case.

Conclusions:

  • The Mermin-Wagner theorem can be inverted on specific graph structures, allowing for spontaneous symmetry breaking.
  • Transient on the average graphs provide a general framework for observing symmetry breaking phenomena.
  • This work offers a new perspective on phase transitions in disordered and inhomogeneous systems.