Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations
arXiv:0905.4417 · doi:10.1016/j.nuclphysb.2009.06.021
Abstract
We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross-Neveu model with Wilson fermions is simulated using the recent `worm' technique on the loop gas or all-order hopping representation of the fermions. An algorithm is formulated that includes the Gross-Neveu interaction for N fermion species. The critical line m_c(g) is constructed for a range of couplings at N = 6 and for N = 2, the Thirring model, as examples.
arXiv comment21 pages, 1 figure. Typos corrected and a few sentences improved. To appear in Nucl. Phys. B [FS]
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