Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory

We consider perturbation of a conformal field theory by a pair of relevant logarithmic operators and calculate the beta function up to two loops. We observe that the beta function can not be derived from a potential. Thus the renormalization group trajectories are not always along decreasing values of the central charge. However there exists a domain of structure constants in which the c-theorem still holds.Comment: 10 pages, latex, no figures, some references are added, The role of coefficients of the OPE in LCFT on the beta-functions are disscuse

Immigration and Human Development: Evidence from Lebanon

This paper takes Lebanon as a case study to examine the relationship between human development and immigration. It examines this issue from both ends: the sending and the receiving countries. The author suggests that by developing the concept of a diasporic civil society and a diasporic public sphere, a significant aspect of the relationship between human development and immigration is illuminated especially at the level of political, social and cultural capitals. The paper also argues that the double impact of the home country and that of destination has a lot to say about the influence of immigration on human development in Lebanon. In examining Australia as a destination country, the paper shows the particular impact that globalisation and September 11 have lately had on the capacity of the Lebanese migrants for human development. Finally, the paper concludes by showing the extent to which the diasporic civil society compensates for the ‘negligent’ character of the Lebanese state in the context of human development.Lebanese diaspora, human development, diasporic civil society, diasporic public sphere, economic and social capitals

The Logarithmic Conformal Field Theories

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any $n$-- point function containing the logarithmic field in terms of ordinary $n$--point functions. At last, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation.Comment: 17 pages ,latex , some minor changes, to appear in Nucl. Phys.

Multi-scale Correlation Functions in Strong Turbulence

Under the framework of V. Yakhot [Phys.Rev.E, {\bf57}, 1737 (1998)] modelling of intermittent structure functions in fully developed turbulence and based on the experimentally supported Markovian nature of turbulence cascades [R.Friedrich and J.Peinke, Phys.Rev.Lett, {\bf 78}, 863 (1997)], we calculate the multiscaling correlation functions. Fusion rules [V.S.L'vov and I. Procaccia, Phys.Rev.Lett. {\bf 76}, 2898 (1996)] which are experimentally tested [R. Benzi, L. Biferale, and F. Toschi, Phys.Rev.Lett. {\bf 80}, 3244 (1998)] to be compatible with almost uncorrelated multiplicative process can analyticaly be supported by direct calculations.Comment: 4 pages, revtex, two postscript figures, submitted to PR

Phase Transition in a Self--Gravitating Planar Gas

We consider a gas of Newtonian self-gravitating particles in two-dimensional space, finding a phase transition, with a high temperature homogeneous phase and a low temperature clumped one. We argue that the system is described in terms of a gas with fractal behaviour.Comment: corrections made and discussions enlarged; to appear P.L.

Quenched Averaged Correlation Functions of the Random Magnets

It is shown that the ratios of the quenched averaged three and four-point correlation functions of the local energy density operator to the connected ones in the random-bond Ising model approach asymptotically to some $universal$ functions. We derive the explicit expressions of these universal functions. Moreover it is shown that the individual logarithmic operators have not any contribution to the connected correlation functions of the disordered Ising model.Comment: 4 pages, twocolumn, to appear in Nucl. Physics

Logarithmic N=1 superconformal field theories

We study the logarithmic superconformal field theories. Explicitly, the two-point functions of N=1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more) Jordan block(s) have been obtained. Using the well known three-point fuctions of N=1 superconformal field theory (SCFT), three-point functions of N=1 LSCFT are obtained. The general form of N=1 SCFT's four-point functions is also obtained, from which one can easily calculate four-point functions in N=1 LSCFT.Comment: 10 pages, LaTeX file, minor revisions made, to appear in Phys. Lett.

Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.Comment: 9 pages, LaTeX, some misprints are corrected, to be published in Phys. Lett.