Field theory of scaling lattice models. The Potts antiferromagnet

In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T->0 is argued to be described exactly by the sine-Gordon field theory at a specific value of the coupling. The solution of the scaling ferromagnetic case is recalled for comparison. The field theory describing the crossover from antiferromagnetic to ferromagnetic behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200

Four-boson scale near a Feshbach resonance

We show that an independent four-body momentum scale $\mu_{(4)}$ drives the tetramer binding energy for fixed trimer energy (or three-body scale $\mu_{(3)}$) and large scattering length ($a$). The three- and four-body forces from the one-channel reduction of the atomic interaction near a Feshbach resonance disentangle $\mu_{(4)}$ and $\mu_{(3)}$. The four-body independent scale is also manifested through a family of Tjon-lines, with slope given by $\mu_{(4)}/\mu_{(3)}$ for $a^{-1}=0$. There is the possibility of a new renormalization group limit cycle due to the new scale

Finite temperature results on the 2d Ising model with mixed perturbation

A numerical study of finite temperature features of thermodynamical observables is performed for the lattice 2d Ising model. Our results support the conjecture that the Finite Size Scaling analysis employed in the study of integrable perturbation of Conformal Field Theory is still valid in the present case, where a non-integrable perturbation is considered.Comment: 9 pages, Latex, added references and improved introductio

Dynamical nature of the nuclear pseudospin and its isospin asymmetry

Pseudospin symmetry in nuclei is investigated by solving the Dirac equation with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin interaction with a pseudospin-orbit term in a Schroedinger-like equation for the lower component of the Dirac spinor. We show that this term gives a large contribution to the energy splittings of pseudospin partners, so that the near pseudospin degeneracy arises from a significant cancellation among the different terms in that equation. This is a manifestation of the dynamical character of this symmetry in the nucleus. We analyze the isospin dependence of the pseudospin symmetry in a nuclear isotope chain by including a vector-isovector potential V_rho and a Coulomb potential and conclude that V_rho gives the main contribution to the observed pseudospin isospin asymmetry.Comment: 4 pages, 2 figures, uses World Scientific style file. Contribution presented at the VIII International Workshop on Hadron Physics, Bento Goncalves, RS, Brazil, April 14-19, 2002. To be published by World Scientific in the proceedings of the "International Workshop on Hadron Physics 2002

Effective range from tetramer dissociation data for cesium atoms

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated to effective range corrections. The effective range correction is extracted, with a weighted average given by 3.9$\pm 0.8 R_{vdW}$, where $R_{vdW}$ is the van der Waals length scale; which is consistent with the van der Waals potential tail for the $Cs_2$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.Comment: A section for two-, three- and four-boson bound state formalism is added, accepted for publication in Phys. Rev.

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

Point-Coupling Models from Mesonic Hypermassive Limit and Mean-Field Approaches

In this work we show how nonlinear point-coupling models, described by a Lagrangian density that presents only terms up to fourth order in the fermion condensate $(\bar{\psi}\psi)$, are derived from a modified meson-exchange nonlinear Walecka model. The derivation can be done through two distinct methods, namely, the hypermassive meson limit within a functional integral approach, and the mean-field approximation in which equations of state at zero temperature of the nonlinear point-coupling models are directly obtained.Comment: 18 pages. Accepted for publication in Braz. J. Phy

Long range correlations generated by phase separation. Exact results from field theory

We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation generates long range correlations in the direction parallel to the interface, and determine their exact analytic form. The latter leads to specific contributions to the structure factor of the interface

Optical characterization of homogeneous and heterogeneous intralipid-based samples

Different scattering processes take place when photons propagate inside turbid media. Many powerful experimental techniques exploiting these processes have been developed and applied over the years in a large variety of situations from fundamental and applied research to industrial applications. In the present paper, we intend to take advantage of Static Light Scattering (SLS), Dynamic Light Scattering (DLS), and Time-Resolved Transmittance (TRT) for investigating all the different scattering regimes by using scattering suspensions in a very large range of scatterer concentrations. The suspensions were prepared using Intralipid 20%, a material largely employed in studies of the optical properties of turbid media, with concentrations from 10-5% to 50%. By the analysis of the angular and temporal dependence of the scattered light, a more reliable description of the scattering process occurring in these samples can be obtained. TRT measurements allowed us to obtain information on the reduced scattering coefficient, an important parameter largely used in the description of the optical properties of turbid media. TRT was also employed for the detection of inclusions embedded in Intralipid suspensions, by using a properly designed data analysis. The present study allowed us to better elucidate the dependence of scattering properties of Intralipid suspensions in a very large concentration range and the occurrence of the different scattering processes involved in the propagation of light in turbid media for the first time to our knowledge. In so doing, the complementary contribution of SLS, DLS, and TRT in the characterization of turbid media from an optical and structural point of view is strongly evidenced