A geometric generalization of field theory to manifolds of arbitrary dimension

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for , while leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as .Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model. Received: 15 October 1998 / Accepted: 4 November 1998     

On the universal behavior of two-dimensional Ising spin glasses

Ising spin glasses are studied, at zero temperature, on a hierarchical lattice as an approach to the square lattice. The stiffness exponent y, which governs the behavior of the interactions under changes of scale, is computed for several distinct continuous symmetric probability distributions for the couplings. All distributions considered lead to the same estimates, i.e., the exponent y is universal. Our results are compared with other estimates available for the two-dimensional Gaussian Ising spin glass.     

Non-perturbative renormalization group for simple fluids

We present a new non-perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and also in the framework of two equivalent scalar field theories. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theory [Adv. Phys. 44, 211 (1995)] but, however, does not suffer from its shortcomings at subcritical temperatures. In the framework of a new canonical field theory for the liquid state developed with that aim, our construction identifies with the effective average action approach developed recently [Phys. Rep. 363 (2002)].     

Surname distribution in population genetics and in statistical physics

Surnames tend to behave like neutral genes, and their distribution has attracted a growing attention from genetists and physicists. We review the century-long history of surname studies and discuss the most recent developments. Isonymy has been regarded as a tool for the measurement of consanguinity of individuals and populations and has been applied to the analysis of migrations. The analogy between patrilineal surname transmission and the propagation of Y chromosomes has been exploited for the genetic characterization of families, communities and control groups. Surname distribution is the result of a stochastic dynamics, which has been studied either as a Yule process or as a branching phenomenon: both approaches predict the asymptotic power-law behavior which has been observed in many empirical researches. Models of neutral evolution based on the theory of disordered systems have suggested the application of field-theoretical techniques, and in particular the Renormalization Group, to describe the dynamics leading to scale-invariant distributions and to compute the related (critical) exponents.     

Theory of Tunneling Magnetoresistance

Rigorous theory of the tunneling magnetoresistance (TMR) based on the real-space Kubo formula and fully realistic tight-binding bands fitted to an ab initio band structure is described. It is first applied to calculate the TMR of two Co electrodes separated by a vacuum gap. The calculated TMR ratio reaches , 65% in the tunneling regime but can be as high as 280% in the metallic regime when the vacuum gap is of the order of the Co interatomic distance (abrupt domain wall). It is also shown that the spin polarization P of the tunneling current is negative in the metallic regime but becomes positive P , 35% in the tunneling regime. Calculation of the tunneling magnetoresistance of an epitaxial Fe/MgO/Fe(001) junction is also described. The calculated optimistic TMR ratio is in excess of 1000% for an MgO barrier of , 20 atomic planes and the spin polarization of the tunneling current is positive for all MgO thicknesses. It is also found that spin-dependent tunneling in an Fe/MgO/Fe(001) junction is not entirely determined by states at the o point ( k =0) even for MgO thicknesses as large as , 20 atomic planes. Finally, it is demonstrated that the TMR ratio calculated from the Kubo formula remains nonzero when one of the Co electrodes is covered with a copper layer. It is shown that non-zero TMR is due to quantum well states in the Cu layer which do not participate in transport. Since these only occur in the down-spin channel, their loss from transport creates a spin asymmetry of electrons tunneling from a Cu interlayer, i.e. non-zero TMR. Numerical modeling is used to show that diffuse scattering from a random distribution of impurities in the barrier may cause quantum well states to evolve into propagating states, in which case the spin asymmetry of the nonmagnetic layer is lost and with it the TMR.     

Quantum critical properties in the topological Ginzburg–Landau theory of self-dual Josephson junction arrays

This paper examines the multicritical behavior of a generalized U(_N1)×U(_N2)$U\left(N_1\right)\times U\left(N_2\right)$ Ginzburg–Landau theory containing two multicomponent complex fields which couple differently to two gauge fields described by two Maxwell terms and one mixed-Chern–Simons term. This model is relevant to the dynamics of Cooper pairs and vortices in a self-dual Josephson junction array system near its superconductor–insulator transition. We develop a renormalization group flow at fixed dimension and obtain the beta functions at one loop when both disorder fields are critical. Two sets of infrared-stable charged fixed points solutions are found for N>_Nc$N>N_c$: partially charged solutions with respect to the gauge fields exist with _Nc=35.6$N_c=35.6$, and fully charged solutions exist with _Nc=12.16$N_c=12.16$. We show that fine tuning the ratio of the two energy scales in the model has the effect of reducing the critical number _Nc$N_c$ and thus enlarges the region where the quantum phase transition is continuous. It is also found that the decoupled fixed point which is stable in the neutral case is no longer attainable in the presence of fluctuating gauge fields. We probe the conductivity at the critical point and show that it has a universal character determined by the renormalization group infrared-stable fixed-point values of the gauge couplings.     

Bose gases near resonance: Renormalized interactions in a condensate

Bose gases at large scattering lengths or beyond the usual dilute limit for a long time have been one of the most challenging problems in many-body physics. In this article, we investigate the fundamental properties of a near-resonance Bose gas and illustrate that three-dimensional Bose gases become nearly fermionized near resonance when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose metastability. The instability and accompanying maximum are shown to be a precursor of the sign change of g₂$g_2$, the renormalized two-body interaction between condensed atoms. g₂$g_2$ changes from effectively repulsive to attractive when approaching resonance from the molecular side, even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length. We carry out our studies of Bose gases via applying a self-consistent renormalization group equation which is further subject to a boundary condition. We also comment on the relation between the approach here and the diagrammatic calculation in an early article [D. Borzov, M.S. Mashayekhi, S. Zhang, J.-L. Song, F. Zhou, Phys. Rev. A 85 (2012) 023620].     

Three-dimensional dilute Bose liquid at finite temperature: a Renormalization Group approach

We consider the influence of temperature on the critical behavior of a weakly interacting three dimensional Bose system. Using the flow equations of the Renormalization Group and a Φ⁴ model with dynamical critical exponent z?=?2, we calculated the critical exponent ν, and the thermodynamical parameters near the critical temperature, taking in consideration the quantum effects. The quantum effects considered using this method gives for ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔT _c was obtained, in the lowest-order approximation, and turns out to be proportional to the scattering length.     

Leading logarithms in the anomalous sector of two-flavour QCD

We add the Wess–Zumino–Witten term to the N=3$N=3$ massive nonlinear sigma model and study the leading logarithms in the anomalous sector. We obtain the leading logarithms to six loops for π⁰→γ^?γ^?${\pi }^0\to {\gamma }^{?}{\gamma }^{?}$ and to five loops for γ^?πππ${\gamma }^{?}\pi \pi \pi$. In addition we extend the earlier work on the mass and decay constant to six loops and the vector form factor to five loops. We present numerical results for the anomalous processes and the vector form factor. In all cases the series are found to converge rapidly.