Matrix Model of Strength Distribution: Extension and Phase Transition

In this work we extend a previous study of matrix models of strength distributions. We still retain the nearest neighbor coupling mode but we extend the values the coupling parameter v. We consider extremes, from very smal v to very large v. We first use the same transiiton operator as before \textless{}n T(n+1)\textgreater{} =constat(=1). For this case we get an exponential decreasefor small v but we get a phase transition beyond v=10. In that case we get an even-odd effect-separate exponentials for even n and for odd n. We now also consider also the dipole choice--where \textless{}nT(n+1)\textgreater{} = \(\sqrt{(n+1)}\) .