Spin ½ model in statistical mechanics and relation to a truncation of the Riemann ξ function in the Riemann Hypothesis

Abstract

In the search for a solution to the Riemann Hypothesis, we have studied an approach that connects the Riemann Problem with physical modeling that refers to statistical mechanics. Thus, we study the relation between a truncation of the Riemann ξ function in the variable z = 1-1/s, where s is the usual complex variable (s=Re(s)+i·Im(s) = ρ + i·t) and the partition function of a ferromagnetic spin 1/2 model on a circle C with long-range interaction, to give a concrete look at a strategy for a possible proof of the Riemann Hypothesis.