Higher-Order Fermion Interactions in Effective Field Theories for Phase Transitions

TL;DR

This paper explores how higher-order fermion interactions, especially 8-fermion terms, influence phase transition types and behaviors in effective theories similar to BCS, revealing significant deviations and potential phenomenological implications.

Contribution

It demonstrates the effects of 8-fermion interactions on phase transition order and properties within effective field theories related to superconductivity.

Findings

Higher-order fermion interactions can change phase transition order.

Theories can exhibit both second-order and first-order transitions.

Superconducting gap behavior can deviate from BCS predictions.

Abstract

We investigate the impact of higher-order fermionic deformations in phase transitions analogous to those described by the Bardeen-Cooper-Schrieffer (BCS) theory. Focusing specifically on the 8-fermion interaction, we show that this term can have significant consequences. In certain regions of parameter space, the theory continues to exhibit second-order phase transitions with mean-field critical exponents and the same critical temperature; however, the temperature dependence of the superconducting gap can deviate markedly from conventional BCS behavior. In other regions, the theory exhibits first-order phase transitions. We conclude by discussing potential phenomenological applications of these theories.