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

Author:

Danilo Merlini,Luca Rusconi,Massimo Sala,Nicoletta Sala

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.

Publisher

Heighten Science Publications Corporation

Subject

General Chemical Engineering

Reference10 articles.

1. 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. 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. 3. Merlini D, Sala M, Sala N. Riemann wave background. 2019. https://www.researchgate.net/publication/335867792_Riemann_wave_background.

4. 4. Baxter RJ. Exactly Solved Models in Statistical Mechanics. Academic Press. 1974.

5. 5. Broughan K. Equivalents of the Riemann Hypothesis: Volume One: Arithmetic Equivalents. Cambridge University Press. 2017.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3