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.Comment: 49 pages, 8 figure

Critical behavior of vector models with cubic symmetry

We report on some results concerning the effects of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. The analysis of the six-loop three-dimensional series provides an accurate description of the renormalization-group flow.Comment: 6 pages. Talk given at the V International Conference Renormalization Group 2002, Strba, Slovakia, March 10-16 200

Strong coupling analysis of the large-N 2-d lattice chiral models

Two dimensional large-N chiral models on the square and honeycomb lattices are investigated by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling. Indeed in the strong coupling region a quite large range of beta values exists where the fundamental mass agrees, within about 5% on the square lattice and about 10% on the honeycomb lattice, with the continuum predictions in the %%energy scheme.Comment: 16 pages, Revtex, 8 uuencoded postscript figure

The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy

In three-dimensional O(N) models, we investigate the low-momentum behavior of the two-point Green's function G(x) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotational-invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice non-linear O(N) sigma models, 1/N-expansion, field-theoretical methods within the phi^4 continuum formulation. In non-rotational invariant physical systems with O(N)-invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent rho, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At N=\infty one finds rho=2. We show that, for all values of $N\geq 0$, $\rho\simeq 2$. Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small.Comment: 65 pages, revte

Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively

Application of the O(N)O(N)-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional σ\sigma-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these results are obtained using a high-temperature expansion in terms of hyperspherical harmonics. Applications in higher dimensions of the same technique are then discussed.Comment: 59208 bytes uuencoded gzip'ed (expands to 135067 bytes Postscript); 4 pages including all figures; contribution to Lattice '9