Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed… (More)
The number-theoretical spin chain has exactly one phase transition , which is located at inverse temperature cr = 2. There the mag-netization jumps from one to zero. The energy density, being zero in the low temperature phase, grows at least linearly in cr ? .
We present numerical and analytical evidence for a rst-order phase transition of the ferromagnetic spin chain with partition function Z() = (? 1)==() at the inverse temperature cr = 2. In a recent paper 6] we established a link between analytic number theory and classical statistical mechanics by interpreting the quotient Z(s) = (s ? 1)==(s) of Riemann zeta… (More)
We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the temperature is decreased below the (single) critical temperature T c = 1 2 , the magnetization jumps from zero to one.
The quotient (s ? 1)==(s) of Riemann zeta functions is shown to be the partition function of a ferromagnetic spin chain for inverse temperature s.
We analyze the number-theoretical spin chain with partition function Z() = (? 1)==() using the polymer model technique. The nite (grand) canonical chains give bounds for the limit free energy and internal energy. The correlation functions for inverse temperature = ?1 are products of two-point functions. A combinatorial result for general interval graphs is… (More)
We consider motion in a periodic potential in a classical, quantum , and semiclassical context. Various results on the distribution of asymptotic velocities are proven.
We shortly review recent work interpreting the quotient (s ? 1)==(s) of Riemann zeta functions as a dynamical zeta function. The corresponding interaction function (Fourier transform of the energy) has been shown to be ferromagnetic, i.e. positive.
We consider the classical three-dimensional motion in a potential which is the sum of n attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the n centres, we find a universal behaviour for all energies E above a positive threshold. Whereas for n = 1 there are no bounded orbits, and for n = 2 there is just one closed… (More)