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Updated: Jun 12, 2025

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Valdemar Melin1, Yuta Sekiguchi2, Paul Wiegmann3

  • 1Department of Physics, <a href="https://ror.org/026vcq606">KTH Royal Institute of Technology</a>, Stockholm, Sweden.

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|September 20, 2024
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Summary

High baryon charge densities may induce a crystalline phase transition in the two-dimensional Gross-Neveu model. This phase transition is confirmed in the large N limit using the Bethe ansatz, aligning with mean-field predictions.

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Area of Science:

  • Quantum Field Theory
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • The two-dimensional Gross-Neveu model is a theoretical framework used to study quantum field theory phenomena.
  • Previous studies suggested a crystalline phase transition at high baryon charge densities based on mean-field approximations.
  • This transition is analogous to Peierls instability in condensed matter systems.

Purpose of the Study:

  • To rigorously demonstrate the occurrence of a crystalline phase transition in the two-dimensional Gross-Neveu model.
  • To investigate this transition in the large N limit, where N represents the rank of the symmetry group.
  • To connect the exact solution with mean-field approximations.

Main Methods:

  • Exact solution of the two-dimensional Gross-Neveu model.
  • Development of the large N limit of the Bethe ansatz.
  • Analytical construction of the large-N solution.
  • Comparison with the periodic (finite-gap) solution of the Korteweg-de Vries (KdV) equation.

Main Results:

  • The crystalline phase transition is confirmed to occur in the large N limit.
  • The large-N solution derived from the Bethe ansatz precisely matches the results from the mean-field analysis.
  • The analytical solution aligns with the periodic solution of the KdV equation.

Conclusions:

  • The study confirms the crystalline phase transition in the two-dimensional Gross-Neveu model at high baryon densities in the large N limit.
  • The findings bridge the gap between exact solutions and mean-field approximations for this model.
  • The results provide a deeper understanding of phase transitions in quantum field theories.