18-24 June 2017
Palacio de Congresos
Europe/Madrid timezone
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Contribution Parallel

Seminarios 1+2
Applications Beyond QCD

Four-Fermi-Theories in 3 dimensions: Critical flavour number of the massless Thirring model



Primary authors


The Thirring model is a Four-Fermi-Theory with a current-current interaction and $U(2N_\text{f})$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a toy model to study chiral symmetry breaking. In the limit of flavour-number $N_\text{f} \to 1/2$ it is connected to the Gross-Neveau model, which shows a parity-breaking discrete chiral phase transition while in the limit of large $N_\text{f}$, chiral symmetry is not spontaneously broken. The critical flavour number, below which the model shows chiral symmetry breaking, has been obtained with different methods over the last years but so far, the results are not conclusive ranging from $N_\text{f,c}=2$ to $\infty$.

In the talk, we employ fierz transformations to derive an effective potential for an order parameter for chiral symmetry breaking and discuss its properties. Via lattice simulations with exactly chiral fermions we can relate at first undetermined parameters of the potential to chirally invariant observables. With this approach we show that there is no spontaneous chiral symmetry breaking in the Thirring model for integer flavour numbers. For half-integer flavour numbers the model shows a discrete parity-breaking phase transition up to some critical flavour number which we present in the talk.

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Applications Beyond QCD