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Surely You're Joking Mr. Feynman has Feynman ascribing to Onsager the following quote (during the International Conference of Theoretical Physics in Kyoto, in 1953):

"We should tell Feynman that nobody has ever figured out the order of any transition correctly from first principles."

Is there reason to believe/disbelieve Onsager said this? Was this true at the time? When did someone first correctly show the order of a phase transition from first principles? (I realize "show" probably has in this case multiple interpretations corresponding to different levels of rigour required I would leave this open to those answering.)

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  • $\begingroup$ Is there a date or a period for that quote? $\endgroup$
    – Mauricio
    Oct 19, 2023 at 23:19
  • $\begingroup$ From aip.org/history-programs/niels-bohr-library/oral-histories/… I think it was during the 1953 meeting in Japan. $\endgroup$
    – Kvothe
    Oct 20, 2023 at 9:39
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    $\begingroup$ The exchange happened at the International Conference of Theoretical Physics in Kyoto, 1953, where Feynman was presenting his Atomic Theory of Liquid Helium Near Absolute Zero. What Onsager said was true at the time and may still be true if one really wants it "from first principles". Microscopic reductions of macroscopic behavior are notoriously intractable. $\endgroup$
    – Conifold
    Oct 20, 2023 at 9:48
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    $\begingroup$ @Conifold This is as good as an answer... $\endgroup$ Oct 21, 2023 at 20:36
  • $\begingroup$ "Microscopic reductions of macroscopic behavior are notoriously intractable" : this may be true (I don't know enough physics) but this was done for superconductivity (with a Nobel prize); see en.wikipedia.org/wiki/BCS_theory . @Conifold $\endgroup$ Oct 22, 2023 at 12:44

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First, the source linked by @Kvothe in a comment provides a wording that is (significantly) different from that in the OP.

Second, I can only guess what Onsager meant, but possibly that was about there being no good theoretical description of phase transitions in three-dimensional models based on calculations using, say, the canonical ensemble. Since 1953, there has been tremendous progress. @MikhailKatz mentioned BCS theory of conductivity; the renormalization group and $\epsilon$-expansion methods were developed. I don't work in this area anymore, but I believe there are now excellent expansions for critical indices. Onsager himself obtained an analytical solution for the phase transition in the two-dimensional Ising model in 1944.

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