Scaling and duality in the superconducting phase transition

The field theoretical approach to duality in the superconducting phase transition is reviewed. Emphasis is given to the scaling behavior, and recent results are discussed.Comment: ws LaTex, 9 pages, 1 figure; published in "Fluctuating Paths and Fields", Festschrift dedicated to Hagen Kleinert on the occasion of his 60th birthday, Edited by W. Janke et al. (World Scientific, Singapore, 2001

Dimensional transmutation and symmetry breaking in Maxwell- Chern-Simons scalar QED

The mechanism of dimensional transmutation is discussed in the context of Maxwell-Chern-Simons scalar QED. The method used is non-perturbative. The effective potential describes a broken symmetry state. It is found that the symmetry breaking vacuum is more stable when the Chern-Simons mass is different from zero. Pacs number: 11.10.Ef, 11.10.Gh.Comment: e-mail: [email protected]

Multifractal Properties of Aperiodic Ising Model: role of geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing a real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(alpha) spectra being shifted to higher values of alpha when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(alpha) function and agree with previous results obtained by the quite distinct transfer matrix approach.Comment: 10 pages, 7 figures, 3 Tables, 17 reference

A note on the phase transition in a topologically massive Ginzburg-Landau theory

We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied for this model. It is found that the topological mass, $\theta$, drives the system into different regimes of phase transition. For instance, there is a $\theta_{c}$ such that for $\theta<\theta_{c}$ a fluctuation induced first order phase transition occurs. On the other hand, for $\theta>\theta_{c}$ only the second order phase transition exists. The 1-loop renormalization group analysis gives further insight to this picture. The fixed point structure exhibits tricritical and second order fixed points.Comment: Revised version; uses a more physical parametrization of the renormalization group equations; new references added; one figure added; EuroLatex, 6 page

A non-perturbative approach to the Coleman- Weinberg mechanism in massless scalar QED

We rederive non-perturbatively the Coleman-Weinberg expression for the effective potential for massless scalar QED. Our result is not restricted to small values of the coupling constants. This shows that the Coleman- Weinberg result can be established beyond the range of validity of perturbation theory. Also, we derive it in a manifestly renormalization group invariant way. It is shown that with the derivation given no Landau ghost singularity arises. The finite temperature case is discussed. Pacs number: 11.10.Ef,11.10.Gh

The "glass transition'' as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse

Topological defects are typically quantified relative to ordered backgrounds. The importance of these defects to the understanding of physical phenomena including diverse equilibrium melting transitions from low temperature ordered to higher temperatures disordered systems (and vice versa) can hardly be overstated. Amorphous materials such as glasses seem to constitute a fundamental challenge to this paradigm. A long held dogma is that transitions into and out of an amorphous glassy state are distinctly different from typical equilibrium phase transitions and must call for radically different concepts. In this work, we critique this belief. We examine systems that may be viewed as simultaneous distribution of different ordinary equilibrium structures. In particular, we focus on the analogs of melting (or freezing) transitions in such distributed systems. The theory that we arrive at yields dynamical, structural, and thermodynamic behaviors of glasses and supercooled fluids that, for the properties tested thus far, are in qualitative and quantitative agreement with experiment. We arrive at a prediction for the viscosity and dielectric relaxations that is universally satisfied for all experimentally measured supercooled liquids and glasses over 15 decades.Comment: 21 pages, 2 figure