691 research outputs found
Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model
We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio
model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean
dimensions. Different model equations of state, corresponding to different
theoretical scenarios, are tested against the order parameter data. The results
are sensitive to necessary assumptions about the shape and extent of the
scaling region. Our best fits favour a trivial scenario in which the
logarithmic corrections are qualitatively similar to those predicted by the
large N_f approximation. This is supported by a separate analysis of finite
volume corrections for data taken directly in the chiral limit.Comment: 37 pages LaTeX (RevTeX) including 12 .eps figure
Lattice Study of Dense Matter with Two Colors and Four Flavors
We present results from a simulation of SU(2) lattice gauge theory with N_f=4
flavors of Wilson fermion and non-zero quark chemical potential mu, using the
same 12^3x24 lattice, bare gauge coupling, and pion mass in cut-off units as a
previous study with N_f=2. The string tension for N_f=4 is found to be
considerably smaller implying smoother gauge field configurations.
Thermodynamic observables and order parameters for superfluidity and color
deconfinement are studied, and comparisons drawn between the two theories.
Results for quark density and pressure as functions of mu are qualitatively
similar for N_f=2 and N_f=4; in both cases there is evidence for a phase in
which baryonic matter is simultaneously degenerate and confined. Results for
the stress-energy tensor, however, suggest that while N_f=2 has a regime where
dilute matter is non-relativistic and weakly-interacting, N_f=4 matter is
relativistic and strongly-interacting for all values of mu above onset.Comment: Horizontal axes of several figures rescaled. Version accepted for
publicatio
Four - Fermi Theories in Fewer Than Four Dimensions
Four-fermi models in dimensionality exhibit an ultra-violet stable
renormalization group fixed point at a strong value of the coupling constant
where chiral symmetry is spontaneously broken. The resulting field theory
describes relativistic fermions interacting non-trivially via exchange of
scalar bound states. We calculate the corrections to this picture,
where is the number of fermion species, for a variety of models and
confirm their renormalizability to this order. A connection between
renormalizability and the hyperscaling relations between the theory's critical
exponents is made explicit. We present results of extensive numerical
simulations of the simplest model for , performed using the hybrid Monte
Carlo algorithm on lattice sizes ranging from to . For
species of massless fermions we confirm the existence of a second order phase
transition where chiral symmetry is spontaneously broken. Using both direct
measurement and finite size scaling arguments we estimate the critical
exponents , , and . We also investigate symmetry
restoration at non-zero temperature, and the scalar two-point correlation
function in the vicinity of the bulk transition. All our results are in
excellent agreement with analytic predictions, and support the contention that
the expansion is accurate for this class of models.Comment: CERN-TH.6557/92 ILL-(TH)-92-\# 19, 60 pages, 18 figures (not
included
Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential
We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density
(chemical potential mu =/= 0). It is possible to formulate this model with a
real action and therefore to perform standard hybrid Monte Carlo simulations
with mu =/= 0 in the functional measure. We compare the physical observables
from these simulations with simulations using the Glasgow method where the
value of mu in the functional measure is fixed at a value mu_upd. We find that
the observables are sensitive to the choice of mu_upd. We consider the
implications of our findings for Glasgow method QCD simulations at mu =/= 0. We
demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu
model is fundamentally different from that in QCD. We find that this difference
explains why there is an unphysical transition in QCD simulations at mu =/= 0
associated with the pion mass scale whereas the transition in the Gross-Neveu
model occurs at a larger mass scale and is therefore consistent with
theoretical predictions. We note classes of theories which are exceptions to
the Vafa-Witten theorem which permit the possibility of formation of baryon
number violating diquark condensates.Comment: 28 pages RevTe
Numerical Study of the Two Color Attoworld
We consider QCD at very low temperatures and non-zero quark chemical
potential from lattice Monte Carlo simulations of the two-color theory in a
very small spatial volume (the attoscale). In this regime the quark number
rises in discrete levels in qualitative agreement with what is found
analytically at one loop on S3xS1 with radius R_S3 << 1/{\Lambda}_QCD. The
detailed level degeneracy, however, cannot be accounted for using weak coupling
arguments. At each rise in the quark number there is a corresponding spike in
the Polyakov line, also in agreement with the perturbative results. In addition
the quark number susceptibility shows a similar behaviour to the Polyakov line
and appears to be a good indicator of a confinement-deconfinement type of
transition.Comment: 18 pages, 10 figure
Electromagnetic Self-Duality in a Lattice Model
We formulate a Euclidean lattice theory of interacting elementary spin-half
electric and magnetic charges, which we refer to as electrons and magnetic
monopoles respectively. The model uses the polymer representation of the
fermion determinant, and exhibits a self-dual symmetry provided electric charge
and magnetic charge obey the minimal Dirac quantisation condition
. In a hopping parameter expansion at lowest order, we show that
virtual electron and monopole loops contribute radiative corrections of
opposite sign to the photon propagator. We argue that in the limit ,
fermion mass , the model describes QED together with strongly
interacting monopoles whose chiral symmetry is spontaneously broken. Prospects
for the existence of an interacting continuum limit at the self-dual point
are discussed.Comment: 29 pages plain TeX, 2 PostScript figures included using psfi
Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model
We investigate spectral functions extracted using the Maximum Entropy Method
from correlators measured in lattice simulations of the (2+1)-dimensional
four-fermion model. This model is particularly interesting because it has both
a chirally broken phase with a rich spectrum of mesonic bound states and a
symmetric phase where there are only resonances. In the broken phase we study
the elementary fermion, pion, sigma and massive pseudoscalar meson; our results
confirm the Goldstone nature of the pi and permit an estimate of the meson
binding energy. We have, however, seen no signal of sigma -> pi pi decay as the
chiral limit is approached. In the symmetric phase we observe a resonance of
non-zero width in qualitative agreement with analytic expectations; in addition
the ultra-violet behaviour of the spectral functions is consistent with the
large non-perturbative anomalous dimension for fermion composite operators
expected in this model.Comment: 25 pages, 13 figure
On the Interplay of Monopoles and Chiral Symmetry Breaking in Non-Compact Lattice QED
Non-compact lattice QED is simulated for various numbers of fermion species
ranging from 8 through 40 by the exact Hybrid Monte Carlo algorithm. Over
this range of , chiral symmetry breaking is found to be strongly
correlated with the effective monopoles in the theory. For between 8 and
16 the chiral symmetry breaking and monopole percolation transitions are second
order and coincident. Assuming powerlaw critical behavior, the correlation
length exponent for the chiral transition is identical to that of monopole
percolation. This result supports the conjecture that monopole percolation
``drives" the nontrivial chiral transition. For between 20 and 32, the
monopoles experience a first order condensation transition coincident with a
first order chiral transition. For as large as 40 both transitions are
strongly suppressed. The data at large N_f (N_f \mathrel {\mathpalette \vereq
>} 20) is interpreted in terms of a strongly interacting monopole gas-liquid
transition.Comment: Revtex file, 23 pages, hardcopy figures only
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