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We investigate the discrete chiral transformation of a Majorana fermion on atorus. Depending on the boundary conditions the integration measure can changesign. Taking this anomalous behavior into account we define a chiral orderparameter as a ratio of partition functions with differing boundary conditions.Then the lattice realization of the Gross-Neveu model with Wilson fermions issimulated using the recent `worm' technique on the loop gas or all-orderhopping representation of the fermions. An algorithm is formulated thatincludes the Gross-Neveu interaction for N fermion species. The critical linem_c(g) is constructed for a range of couplings at N = 6 and for N = 2, theThirring model, as examples.

Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations