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Spontaneous SO(2N) symmetry breaking in Gross-Neveu model

Published on:

14 March 2024

Primary Category:

High Energy Physics - Theory

Paper Authors:

SangEun Han,

Igor F. Herbut

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Key Details

Gross-Neveu model has continuous transition at gc1 preserving SO(2N) symmetry

Mean field theory predicts second transition at gc2 breaking SO(2N) to SO(NxSO(N)

Additional quartic terms added to Gross-Neveu model with multiple fermion copies

For many copies, renormalization group has 3 critical points, including gc2 transition

Below critical number of copies, only gc1 implies diverging susceptibility

Suggests gc2 transition in original model made first-order by fluctuations

AI generated summary

Spontaneous SO(2N) symmetry breaking in Gross-Neveu model

The Gross-Neveu model for interacting Dirac fermions in 2+1 dimensions suffers a continuous phase transition preserving SO(2N) symmetry and breaking a discrete symmetry at one critical coupling gc1. At a different critical coupling gc2, mean field theory predicts SO(2N) itself breaks to SO(N)xSO(N). This paper investigates gc2 via a reformulated Gross-Neveu model with additional quartic interaction terms. For multiple copies of fermions, three distinct critical points emerge, including the gc2 transition. Below a critical number of copies, only the original gc1 transition implies a diverging susceptibility. This suggests fluctuations make the gc2 transition first-order in the original Gross-Neveu model.

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