International Journal of Modern Physics B

In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional QCPs will be discussed: (1) The transition between topological order and semiclassical spin ordered phase; (2) The transition between topological order and valence bond solid phase; (3) The direct second order transition between different competing orders. We focus on the field theory and universality class of these unconventional QCPs. Relation of these QCPs with recent numerical simulations and experiments on quantum frustrated magnets are also discussed.

There are a substantial number of empirical relations that began with the identification of a pattern in data; were shown to have a terse power-law description; were interpreted using existing theory; reached the level of "law" and given a name; only to be subsequently fade away when it proved impossible to connect the "law" with a larger body of theory and/or data. Various forms of allometry relations (ARs) have followed this path. The ARs in biology are nearly two hundred years old and those in ecology, geophysics, physiology and other areas of investigation are not that much younger. In general if X is a measure of the size of a complex host network and Y is a property of a complex subnetwork embedded within the host network a theoretical AR exists between the two when Y = aX^b. We emphasize that the reductionistic models of AR interpret X and Y as dynamic variables, albeit the ARs themselves are explicitly time independent even though in some cases the parameter values change over time. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret X and Y as averages to yield the empirical AR: 〈Y〉 = a〈X〉^b. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of theoretical ARs in living networks is slightly more than a decade old and although well received it has not been universally accepted. An alternate perspective is given by the empirical AR that is derived using linear regression analysis of fluctuating data sets. We emphasize that the theoretical and empirical ARs are not the same and review theories "explaining" AR from both the reductionist and statistical fractal perspectives. The probability calculus is used to systematically incorporate both views into a single modeling strategy. We conclude that the empirical AR is entailed by the scaling behavior of the probability density, which is derived using the probability calculus.

The hybrid structure of polymeric nitrogen chains and carbon nanotube bundle (CNTB) is studied using first-principle calculations. Our finite temperature molecular dynamics simulations show the hybrid system to be very stable at room temperature. The detailed electronic structure is also revealed in this study. According to the calculated electronic structure, the room temperature stabilization of the hybrid material has been demonstrated to originate from the electron transfer from carbon nanotubes (CNTS) to polymeric nitrogen chains. The present work provides a new way to synthesize nitrogen-based high-energy-density materials (HEDM).

High pressure effect on the structural evolution properties of intermetallic compounds PtX (X = Si, Ge, Sn AND Pb) was studied based on the first principle density functional theory. The compressibility of PtSi and PtGe under high pressure presents anisotropic behavior. The crystal stacking characteristic of the PtX (X = Si and Ge) along the three axes may be responsible for their anisotropic axial compressibility under high pressure. The sequence of axial compressibility for PtSi is c < a < b, whereas PtGe exhibits the sequence of a < c < b. The pressure derivative of c/a was qualified to be 8.92×10^-4GPa^-1 and 1.38×10^-3GPa^-1 for PtSn and PtPb, respectively. The applied pressure stabilized the crystal structures of PtSn and PtPb.