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 of the coupling parameter v. We consider extremes, from very small v to very large v. We first use the same transition operator as before < nT(n + 1)> = constant(= 1). For this case, we get an exponential decrease for small v, as expected, but we get a phase transition beyond v=10, where we get separate exponentials for even n and for odd n. We now also consider the dipole choice where < nT(n + 1)> = root(n + 1).