Short Communication

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

Danilo Merlini, Luca Rusconi, Massimo Sala and Nicoletta Sala*

Published: 05 June, 2023 | Volume 6 - Issue 1 | Pages: 115-116

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. 

Read Full Article HTML DOI: 10.29328/journal.ijpra.1001058 Cite this Article Read Full Article PDF


  1. Riemann B. On the number of prime numbers below a given size. Monthly reports of the Berlin Academy. In Collected Works, Teubner, Leipzig (1892), Reprinted by Dover, New York (1953). Original manuscript (with English translation). Reprinted in (Borwein et al., 2008) and (Edwards, 1974). 1859.
  2. Merlini D, Rusconi L. Small Ferromagnetic Systems and Polynomial Truncations of the Riemann Function ξ. Chaos and Complexity Letters. 2018; 12(2): 101-122.
  3. Merlini D, Sala M, Sala N. Riemann wave background. 2019. https://www.researchgate.net/publication/335867792_Riemann_wave_background.
  4. Baxter RJ. Exactly Solved Models in Statistical Mechanics. Academic Press. 1974.
  5. Broughan K. Equivalents of the Riemann Hypothesis: Volume One: Arithmetic Equivalents. Cambridge University Press. 2017.
  6. Broughan K. Equivalents of the Riemann Hypothesis: Volume Two: Analytic Equivalents. Cambridge University Press. 2017.
  7. Conrey B. Riemann’s Hypothesis. American Institute of Mathematics. 2019. https://aimath.org/~kaur/publications/90.pdf
  8. Farmer DW. Jensen polynomials are not a plausible route to proving the Riemann Hypothesis. Advances in Mathematics. 2020; 411:108781.
  9. Merlini D, Rusconi L, Sala M, Sala N. Blocks partition analysis: a possible positivity of the Li-Keiper coefficients. Chaos and Complexity Letters. 2022; 16(2): 95-105.
  10. Merlini D, Sala M, Sala N. Primitive Riemann Wave at Re(s) = 0.9 and Application. Chaos and Complexity Letters. 2020; 14(1): 3-32.

Similar Articles

Recently Viewed

Read More

Most Viewed

Read More

Help ?