ChemInform Abstract: Rod‐Like Dispiro(5.1.5.2) Compounds.

Abstract

Rod-Like Dispiro(5.1.5.2) Compounds.-Starting with the dispiro(5.1.5.2)trione (I), a number of sym. and unsym. substituted spiro compounds are synthesized such as is demonstrated for some examples. The formation of the trans-trans isomers of (II), its dicyano analogue, its dibutoxy derivative as well as its diester, e.g. (V), are favored. Some of the compounds functionalized with flexible side groups show narrow liquid-crystal phases. -(BOETTCHER, J.; HARTMANN, R.; VOEGTLE, F.; Chem.

Fixed-point properties of the Ising ferromagnet on the Hanoi networks

“…We are currently developing the RG scheme to investigate more complicated observables to extract insights into the physical origin of these peculiar critical phenomena. Merely the addition of an external field as a generator for magnetic properties already makes the analysis much more complicated by breaking the Z 2 -symmetry, thus allowing for yet another renormalizable bond linking three spins simultaneously [18]. As well, the study of other models spin in this context seems desirable.…”

“…Similar to the step from HN3 to HN5, we can add the emerging bonds L 1 again as an original feature of the network, which we parameterize as in Eq. (18). As a result, we obtain a network that has an average degree of 6 with an exponential distribution of bonds which we will call HN6, accordingly.…”

“…Here, we use an exact real-space renormalization group (RG) to study the ferromagnetic Ising model on the recently introduced set of Hanoi networks [12][13][14]. Hanoi networks have been used to study phenomena as diverse as diffusion [13,14], synchronization [12], the exclusion process [15], percolation [16], quantum transport [17], and the vertex cover problem [18]. These hierarchically constructed networks possess a regular degree or have an exponential degree distribution, akin to the Watts-Strogatz Small Worlds [19].…”