# Monte Carlo Simulation of the Three Dimensional Thirring Model

## TL;DR

This study uses Monte Carlo simulations to explore the three-dimensional Thirring model, revealing chiral symmetry breaking at strong coupling for certain fermion flavors and analyzing phase transition behaviors.

## Contribution

First Monte Carlo analysis of the 3D Thirring model on lattice sizes 8^3 and 12^3, confirming chiral symmetry breaking for N_f=2,4 and examining phase transitions.

## Key findings

- Chiral symmetry breaking occurs for N_f=2,4 at strong coupling.
- Phase transitions are continuous with critical scaling.
- Preliminary results for N_f=6 are inconclusive.

## Abstract

We study the Thirring model in three spacetime dimensions, by means of Monte Carlo simulation on lattice sizes 8^3 and 12^3, for numbers of fermion flavors N_f=2,4,6. For sufficiently strong interaction strength, we find that spontaneous chiral symmetry breaking occurs for N_f=2,4, in accordance with the predictions of the Schwinger-Dyson approach. The phase transitions which occur are continuous and with critical scaling behaviour depending on N_f. For N_f=6 our results are preliminary, and no firm conclusions about the existence or otherwise of chiral symmetry breaking are possible