Critical flavor number of the Thirring model in three dimensions

The Thirring model is a four fermion theory with vector interaction. We study it in three dimensions, where it is closely related to QED and other models used to describe properties of graphene. In addition it is a good toy model to study chiral symmetry breaking, since a phase with broken chiral symmetry is present for the model with one fermion flavour. On the other hand, there is no such phase in the limit of infinitely many fermion flavours. Thus, a transition at some critical flavour number Nfc is expected, where the broken phase vanishes. The model was already studied with different methods, including Schwinger-Dyson, functional renormalization group and lattice approaches. Most studies agree that there is indeed a phase transition from a chirally symmetric phase to a spontaneously broken phase for a small number of fermion flavours. But there is no agreement on the critical flavour number and further details of the critical behaviour. Values of Nfc found in the literature usually range between 2 and 7. All earlier lattice studies were performed with staggered fermions, where it is questionable if the continuum limit of the lattice model has the same chiral symmetry as the continuum model. We present an approach for simulations of the Thirring model with SLAC fermions. With this choice, we can be sure to implement the full chiral symmetry of the continuum model. First results from simulations are shown but do not allow a reliable estimate of Nfc so far.

蒂林模型是一种具有矢量相互作用的四费米子理论。我们在三维空间中对其进行研究，在该维度下它与量子电动力学（QED）以及其他用于描述石墨烯性质的模型密切相关。此外，它是研究手征对称性破缺的一个很好的玩具模型，因为对于具有一种费米子味的模型存在一个手征对称性破缺的相。另一方面，在费米子味无穷多的极限情况下不存在这样的相。因此，预计在某个临界味数$N_{fc}$处会发生转变，此时破缺相消失。该模型已经用不同的方法进行了研究，包括施温格 - 戴森方程、泛函重整化群以及格点方法。大多数研究都认为，对于少量的费米子味，确实存在从手征对称相到自发破缺相的相变。但是对于临界味数以及临界行为的更多细节并没有达成一致。文献中发现的$N_{fc}$值通常在2到7之间。所有早期的格点研究都是用交错费米子进行的，在这种情况下，格点模型的连续极限是否具有与连续模型相同的手征对称性是值得怀疑的。我们提出了一种用斯坦福直线加速器中心（SLAC）费米子模拟蒂林模型的方法。通过这种选择，我们可以确保实现连续模型的完全手征对称性。展示了模拟的初步结果，但到目前为止还无法对$N_{fc}$进行可靠的估计。