43 research outputs found
Three dimensional four-fermion models - A Monte Carlo study
We present results from numerical simulations of three different 3d
four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral
symmetries, respectively. We performed the simulations by using the hybrid
Monte Carlo algorithm. We employed finite size scaling methods on lattices
ranging from 8^3 to 40^3 to study the properties of the second order chiral
phase transition in each model. The corresponding critical coupling defines an
ultraviolet fixed point of the renormalization group. In our high precision
simulations, we detected next-to-leading order corrections for various critical
exponents and we found them to be in good agreement with existing analytical
large-N_f calculations.Comment: 15 pages, 7 figures, and 2 table
Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density
The three-dimensional four-fermion model with a Z_2 chiral symmetry and N=4
fermion species in the system is investigated numerically at non-zero
temparature and chemical potential. The phase diagram in the (chemical
potential, temperature) plane is mapped out quantitatively. A detailed finite
size scaling analysis shows that the zero temperature and non-zero chemical
potential chiral phase transition is first order, whereas the non-zero
temperature and non-zero chemical potential transition remains second order
down to very low temperatures. Quantitative results for the location of the end
of the first order line are given. The simulations at T=0 provided no evidence
for a nuclear liquid-gas transition.Comment: 23 pages, 15 figure
Non-Compact QED_3 with N_f=1 and N_f=4
We present numerical results for non-compact three-dimensional QED for
numbers of flavors N_f=1 and N_f=4.In particular, we address the issue of
whether chiral symmetry is spontaneously broken in the continuum limit, and
obtain a positive answer for N_f=1, with a dimensionless condensate estimated
to be beta^2 ~= O(10^-3), implying that the critical number of
flavors N_fc>1. We also compare the N_f=1 and N_f=4 models by analysing the
transition from strong to weak coupling behaviour using an equation of state
based on a continuous phase transition. While some qualitative differences
emerge, it appears difficult to determine whether N_f=4 lies above or below
N_fc.Comment: 19 pages, 10 figure
Phase diagram of the three-dimensional NJL model
With the exception of confinement the three-dimensional Nambu-Jona-Lasinio
(NJL_3) model incorporates many of the essential properties of QCD. We discuss
the critical properties of the model at nonzero temperature T and/or nonzero
chemical potential . We show that the universality class of the thermal
transition is that of the d=2 classical spin model with the same symmetry. We
provide evidence for the existence of a tricritical point in the
(,temperature) plane. We also discuss numerical results by Hands et al.
which showed that the system is critical for and the diquark
condensate is zero.Comment: 3 pages, To appear in the proceedings of Conference on Quarks and
Nuclear Physics (QNP 2002), Julich, Germany, 9-14 Jun 200
Zero Lattice Sound
We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon
chemical potential mu, using both analytical and numerical methods. In
particular, we study the self-consistent Boltzmann equation in the Fermi liquid
framework using the quasiparticle interaction calculated to O(1/N_f), and find
solutions for zero sound propagation for almost all mu > mu_c, the critical
chemical potential for chiral symmetry restoration. Next we present results of
a numerical lattice simulation, examining temporal correlation functions of
mesons defined using a point-split interpolating operator, and finding evidence
for phonon-like behaviour characterised by a linear dispersion relation in the
long wavelength limit. We argue that our results provide the first evidence for
a collective excitation in a lattice simulation.Comment: 18 pages, 6 figure