TITLE: Examples where physical heuristics led to incorrect answers?
QUESTION [86 upvotes]: I have always been impressed by the number of results conjectured by physicist, based on mathematically non-rigorous reasoning, then (much) later proved correct by mathematicians. A recent example is the $\sqrt{2+\sqrt{2}}$ connective constant of the honeycomb lattice, derived non rigorously by the physicist B. Nienhuis in 1982 and rigorously proved this year by S. Smirnov and H. Duminil-Copin.
I would be interested in knowing examples of results conjectured by physicists and later proved wrong by mathematicians.  Furthermore it would be interesting to understand why physical heuristics can go wrong, and how wrong they can go (for example, were the physicists simply missing an important technical assumption or was the conjecture unsalvagable).

REPLY [5 votes]: In the context of the Abelian sandpile model, in the paper ``Absorbing-state phase transitions in fixed-energy sandpiles'' (https://arxiv.org/abs/cond-mat/0003285) the physicists Vespignani, Dickman, Muñoz, and Zapperi predicted that the threshold density of the fixed energy sandpile should be the same as the stationary density of this model. But in fact this heuristic was refuted in some graphs by Fey, Levine and Wilson (https://arxiv.org/abs/1001.3401v2 and https://arxiv.org/abs/0912.3206). In particular while the two quantities in question appear to be close to one another in the cases of interest to physicists (torus/grid graphs), they aren't the same. The issue is that the threshold density depends on the initial configuration one starts from: the system remembers some of its pre-critical past at criticality. One then suspects that if the system is allowed enough time to mix, the threshold density will be the same as the stationary density. Hence, some more physicists (Poghosyan et al. https://arxiv.org/abs/1104.3548) conjectured that if the total number of grains of sand of the initial configuration goes to negative infinity, in the limit the threshold density and stationary density agree. Levine proved this is the case ("Threshold state and a conjecture of Poghosyan, Poghosyan, Priezzhev and Ruelle" https://arxiv.org/abs/1402.3283). Levine's paper is very well written and he goes over all this history in the introduction.