32382258
Two-dimensional SU(N) x SU(N) chiral models on the lattice. II. The Green's function.
Analytical and numerical methods are applied to principal chiral models on a twodimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied to the evaluation of the two-point correlation function. The momentum-space lattice propagator is constructed with precision O ( β10 ) and an evaluation of the correlation length is obtained for several different definitions. Three-loop weak coupling contributions to the internal energy and to the lattice β and γ functions are evaluated for all N , and the effect of adopting the “energy” definition of temperature is computed with the same precision. Renormalizationgroup improved predictions for the two-point Green’s function in the weak coupling ( continuum ) regime are obtained and successfully compared with Monte Carlo data. We find that strong coupling is predictive up to a point where asymptotic scaling in the energy scheme is observed. Continuum physics is insensitive to the effects of the large N phase transition occurring in the lattice model. Universality in N is already well established for N ∼ 10 and the large N physics is well described by a “hadronization” picture.
14791593
The large-N expansion of unitary-matrix models
The general features of the 1/N expansion in statistical mechanics and 
quantum field theory are briefly reviewed both from the theoretical and from 
the phenomenological point of view as an introduction to a more detailed 
analysis of the large-N properties of spin and gauge models possessing the 
symmetry group $SU(N) \times SU(N)$. 
 An extensive discussion of the known properties of the single-link integral 
(equivalent to YM_2 and one-dimensional chiral models) includes finite-$N$ 
results, the external field solution, properties of the determinant, and the 
double scaling limit. 
 Two major classes of solvable generalizations are introduced: one-dimensional 
closed chiral chains and models defined on a $d-1$ dimensional simplex. In both 
cases large-N solutions are presented with emphasis on their double scaling 
properties. 
 The available techniques and results concerning unitary-matrix models that 
correspond to asymptotically free quantum field theories (two-dimensional 
chiral models and four-dimensional QCD) are discussed, including 
strong-coupling methods, reduced formulations, and the Monte Carlo approach.
122532894
Asymptotic scaling from strong coupling
Strong-coupling analysis of two-dimensional chiral models, extended to 15th 
order, allows for the identification of a scaling region where known continuum 
results are reproduced with great accuracy, and asymptotic scaling predictions 
are fulfilled. The properties of the large-$N$ second-order phase transition 
are quantitatively investigated.
15958724
Mean-field expansion for spin models with medium-range interactions
We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as R -3, R being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches. @ 1999 Elsevier Science B.V. All rights reserved.
14865562
Critical behavior of the three-dimensional XY universality class
We improve the theoretical estimates of the critical exponents for the 
three-dimensional XY universality class. We find alpha=-0.0146(8), 
gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and 
delta=4.780(2). We observe a discrepancy with the most recent experimental 
estimate of alpha; this discrepancy calls for further theoretical and 
experimental investigations. Our results are obtained by combining Monte Carlo 
simulations based on finite-size scaling methods, and high-temperature 
expansions. Two improved models (with suppressed leading scaling corrections) 
are selected by Monte Carlo computation. The critical exponents are computed 
from high-temperature expansions specialized to these improved models. By the 
same technique we determine the coefficients of the small-magnetization 
expansion of the equation of state. This expansion is extended analytically by 
means of approximate parametric representations, obtaining the equation of 
state in the whole critical region. We also determine the specific-heat 
amplitude ratio.
14560737
k-string tensions in SU(N) gauge theories
In the context of four-dimensional SU(N) gauge theories, we study the 
spectrum of the confining strings. We compute, for the SU(6) gauge theory 
formulated on a lattice, the three independent string tensions sigma_k related 
to sources with Z_N charge k=1,2,3, using Monte Carlo simulations. Our results, 
whose uncertainty is approximately 2% for k=2 and 4% for k=3, are consistent 
with the sine formula sigma_k/sigma = sin(k pi/N) / \sin(pi/N) for the ratio 
between sigma_k and the standard string tension sigma, and show deviations from 
the Casimir scaling. 
 The sine formula is known to emerge in supersymmetric SU(N) gauge theories 
and in M-theory. We comment on an analogous behavior exhibited by 
two-dimensional SU(N)xSU(N) chiral models.
15179667
Rigorous treatment of the lattice renormalization problem of fB.
The B-meson decay constant can be measured on the lattice using a 1/m b expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalizaton coefficient Z between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of Z. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point B-meson correlator in the limit of large b-quark mass, we prove that the two schemes give consistent results to order α s
12453573
Resonant conversion of massless neutrinos in supernovae.
It has been noted for a long time that, in some circumstances, massless neutrinos may be mixed in the leptonic charged current. Conventional neutrino oscillation searches in vacuum are insensitive to this mixing. We discuss the effects of resonant massless-neutrino conversions in the dense ! 