Critical phenomena and renormalization-group flow of multi-parameter \Phi^4 field theories

In the framework of the renormalization-group (RG) approach, critical phenomena can be investigated by studying the RG flow of multi-parameter $\Phi^4$ field theories with an $N$-component fundamental field, containing up to 4th-order polynomials of the field. Some physically interesting systems require $\Phi^4$ field theories with several quadratic and quartic parameters, depending essentially on their symmetry and symmetry-breaking pattern at the transition. Results for their RG flow apply to disorder and/or frustrated systems, anisotropic magnetic systems, density wave models, competing orderings giving rise to multicritical behaviors. The general properties of the RG flow in multi-parameter $\Phi^4$ field theories are discussed. An overview of field-theoretical results for some physically interesting cases is presented, and compared with other theoretical approaches and experiments. Finally, this RG approach is applied to investigate the nature of the finite-temperature transition of QCD with $N_f$ light quarks.Comment: 22 pages, Plenary talk at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular sudden changes of the trap size. In order to characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the overlap of the out-of-equilibrium quantum states with the initial ground state. Their asymptotic particle-number dependences show power laws for noninteracting Fermi gases. We also discuss the effects of short-ranged interactions to the power laws of the average work and its square fluctuations, within the Hubbard model and its continuum limit, arguing that they do not generally change the particle-number power laws of the free Fermi gases, in any spatial dimensions.Comment: 16 pages, 5 fig

Critical mass renormalization in renormalized phi4 theories in two and three dimensions

We consider the O(N)-symmetric phi4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the phi4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative series in the massive renormalization scheme, taking into account their Borel summability and the known large-order behavior of the coefficients. The results are in good agreement with those obtained in lattice calculations.Comment: 4 page

Scaling of decoherence and energy flow in interacting quantum spin systems

We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity of a quantum first-order or continuous phase transition. Although the approach is quite general, we consider d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields, as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchanges among the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing the system size.Comment: 16 pages, 9 figure

Randomly dilute spin models: a six-loop field-theoretic study

We consider the Ginzburg-Landau MN-model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N -> 0 which describes the critical behaviour of an M-vector model in the presence of weak quenched disorder. We perform a detailed analysis of the perturbative series for the random Ising model (M=1). We obtain for the critical exponents: gamma = 1.330(17), nu = 0.678(10), eta = 0.030(3), alpha=-0.034(30), beta = 0.349(5), omega = 0.25(10). For M > 1 we show that the O(M) fixed point is stable, in agreement with general non-perturbative arguments, and that no random fixed point exists.Comment: 29 pages, RevTe

Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries

We investigate systems of interacting bosonic particles confined within slab-like boxes of size L^2 x Z with Z<<L, at their three-dimensional (3D) BEC transition temperature T_c, and below T_c where they experience a quasi-2D Berezinskii-Kosterlitz-Thouless transition (at T_BKT < T_c depending on the thickness Z). The low-temperature phase below T_BKT shows quasi-long-range order: the planar correlations decay algebraically as predicted by the 2D spin-wave theory. This dimensional crossover, from a 3D behavior for T > T_c to a quasi-2D critical behavior for T < T_BKT, can be described by a transverse finite-size scaling limit in slab geometries. We also extend the discussion to the off-equilibrium behavior arising from slow time variations of the temperature across the BEC transition. Numerical evidence of the 3D->2D dimensional crossover is presented for the Bose-Hubbard model defined in anisotropic L^2 x Z lattices with Z<<L.Comment: 16 page

Finite size scaling in CP(N-1) models

Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and correlation length are compared and found to agree for small volumes. For large volumes a discrepancy is found and explained as an effect of the physical bound state extension. The leading order finite size effects on the Abelian string tension are computed and compared with simulations finding agreement. Finite size dependence of topological quantities is also discussed.Comment: 22 pages, the figures are missing, on request they will be send by mail or FA

Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions

We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various critical regimes: the infinite-volume critical behavior in the disordered phase, the finite-size scaling limit for homogeneous systems of finite size, and the trap-size scaling limit occurring in 2D bosonic particle systems trapped by an external space-dependent potential.Comment: 16 pages, refs adde