Instantons in Gross-Neveu and Gross-Neveu-Yukawa models

We study fermionic instantons of the Gross-Neveu and the Gross-Neveu-Yukawa models. We derive new solutions for both models and examine the corresponding actions at the fixed points. We further map the solutions on to the sphere and discuss the relation to the Hubbard-Stratonovich approach. Close to the fixed points we compare and identify the results with those obtained in the large <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> </a:math> computation.