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Register a new userZamolodchikovs c-function for the Chiral Gross-Neveu Model
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Authors
Daniel C. Cabra
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We construct the Zamolodchikovs c-function for the Chiral Gross-Neveu Model up to two loops. We show that the c-function interpolates between the two known critical points of the theory, it is stationary at them and it decreases with the running coupling constant. In particular one can infer the non-existence of additional critical points in the region under investigation.
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We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.
The large N limit of the 3-d Gross-Neveu model is here studied on manifolds with positive and negative constant curvature. Using the $zeta$-function regularization we analyze the critical properties of this model on the spaces $S^2 times S^1$ and $H^2times S^1$. We evaluate the free energy density, the spontaneous magnetization and the correlation length at the ultraviolet fixed point. The limit $S^1to R$, which is interpreted as the zero temperature limit, is also studied.
We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized $T$-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the $T$-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.
The phase diagram of the Gross-Neveu (G-N) model in 2+1 dimensions as a function of chemical potential and temperature has a simple curve separating the broken symmetry and unbroken symmetry phases, with chiral symmetry being restored both at high temperature and high density. We study, in leading order in the 1/N expansion, the dynamics of the chiral phase transition for an expanding plasma of quarks in the Gross-Neveu model in 2+1 dimensions assuming boost invariant kinematics. We compare the time evolution of the order parameter (mass of the fermion) for evolutions starting in the unbroken and broken phases. The proper time evolution of the order parameter resembles previous results in the 1+1 dimensional G-N model in the same approximation. The time needed to traverse the transition is insensitive to mu.
We investigate the chiral phase structure of the Gross-Neveu model on a 2-D lattice using the Borici-Creutz fermion action. We present a strong coupling analysis of the Gross-Neveu model and perform a hybrid Monte Carlo simulation of the model with Borici-Creutz fermions. Both analytic and lattice results show a second order chiral phase transition.
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