Ginzburg-Landau approach to the Gross-Neveu model: success and failure

TL;DR

This paper uses a Ginzburg-Landau expansion to analyze the phase diagram of the 1+1 dimensional Gross-Neveu model, highlighting its successes in predicting features and its failures at low temperatures due to the Silver-Blaze phenomenon.

Contribution

It demonstrates the effectiveness and limitations of the Ginzburg-Landau approach in capturing the phase structure of the Gross-Neveu model.

Findings

Accurately predicts several features of the phase diagram at low orders

Improves the crystal phase prediction with higher-order expansions

Fails at very small temperatures due to the Silver-Blaze phenomenon

Abstract

The phase diagram of the Gross-Neveu model in 1+1 dimensions is studied using Ginzburg-Landau expansion. It predicts several features of the exact phase diagram correctly even at low orders. It is shown that increasing the order of the expansion improves the accuracy of the crystal phase except for very small temperatures, where the expansion completely fails regardless of the order of the expansion. The source of this behaviour seems to be related to the Silver-Blaze phenomenon.