No abstract

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N . Three fixed points are identified. The matrix model θ = ∞ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at θ = 0 which describes the disordered-to-uniformordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of θ which is associated with the transition between non-uniform-order and uniform-order phases. IntroductionA noncommutative field theory is a non-local field theory in which we replace the ordinary local point-wise multiplication of fields with the non-local Moyal-Weyl star product [1,2]. This product is intimately related to coherent states [6][7][8], Berezin quantization [9] and deformation quantization [10]. It is also very well understood that the underlying operator/matrix structure of the theory, exhibited by the Weyl map [5], is the singular most important difference with commutative field theory since it is at the root cause of profound physical differences between the two theories. We suggest [3] and references therein for elementary and illuminating discussion of the Moyal-Weyl product and other star products and their relations to the Weyl map and coherent states.Noncommutative field theory is believed to be of importance to physics beyond the standard model and the Hall effect [34] and also to quantum gravity and string theory [35,36]. * Email:ydri@stp.dias.ie, badis.ydri@univ-annaba.org. 1Noncommutative scalar field theories are the most simple, at least conceptually, quantum field theories on noncommutative spaces. Some of the novel quantum properties of noncommutative scalar field theory and scalar phi-four theory are as follows:

The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory.

The lead sulfur (PbS) as thin films were deposited on ordinary glass slides, for different deposition times ranging from 30 to 90 min, and for different molar concentrations of lead nitrate (0.01, 0.05, 0.075 and 0.1) mol / l, at ambient temperature of 55 ° C, using thiourea and lead nitrate as source of S2- and Pb2+ ions respectively and TEA as complexing agent. For different deposition times, the films grow preferentially along (200) direction. With increase in deposition time, and at fixed molar concentration the transmittance remained less than 30% and the optical band gap value decreases from 1.8 to 1.6 eV, while the crystallite size increases from 21.9 to 27.8 nm. For various molar concentrations of lead nitrate and with time deposition equal to 60 min, it was observed that the films grow preferentially along (111) or (200) directions, which depend on the molar concentration. Increasing the concentration of lead nitrate leads to decrease the energy gap from 1.58 to 1.37 eV and increase the crystallite sizes from 28.0 to 32.6 nm.

The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with an emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory.