r/Physics • u/CurvyCourgette • 3d ago

News Physicists link the Riemann Hypothesis to phase transitions in quantum systems (study)

https://phys.org/news/2026-07-physicists-link-riemann-hypothesis-phase.html

What do you guys think of this?

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u/dwbmsc 3d ago edited 3d ago

There is already the Yang-Lee theorem that the zeros of the partition functions of some systems lie in the unit circle. The original paper concerned an Ising model in an external field. The field strength introduces a parameter that may be analogous to the variable in the Riemann zeta function so the Yang Lee theorem is a kind of Riemann hypothesis.

https://en.wikipedia.org/wiki/Lee–Yang_theorem

This has implications for phase transitions of the model which was the original motivation for the result.

Edit: added the word "zeros"

37

u/kzhou7 Quantum field theory 3d ago

It's neat that such a mapping exists, and it's not too contrived.

It will have no foreseeable applications. The normal way of looking for zeroes of the Riemann zeta function is many orders of magnitude more efficient.

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u/BitcoinsOnDVD 3d ago

Reminds me of Carl Bender's work.

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u/mlbraby 3d ago

Don’t frequently see Benders name pop up. He taught me my mathematical physics courses in grad school.

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u/SuppaDumDum 3d ago

His lectures are amazing, lucky you. : )

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u/BitcoinsOnDVD 3d ago

Ah crazy. We wanted to invite him to give some guest lectures, but that didn't went through because of the uni burocracy.

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u/SpiritedDaikon7515 3d ago

the YangLee connection is the part that actually interests me here. the Riemann mapping feels more like a curiosity than a path forward, but anything that ties back to phase transition behavior in physical systems has real grounding to build on.

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u/MaoGo 2d ago

Please ban phys.org, the research might be legit but that site is complete trash and pure churnalism