It should be emphasized that this is not the $E_8$ of heterotic string theory or the $E_8$ gauge group in various grand unified theories. It comes out of something much more down-to-earth, namely solid state physics. The $E_8$ in this story is an unexpected symmetry of the two-dimensional Ising model in a magnetic field that was discovered by Zamolodchikov in 1989.

The Ising model was devised as a simple mathematical model that, it was hoped, would exhibit a ferromagnetic critical point. This turned out to be the case, as Onsager showed in 1944. The model is connected to a lot of beautiful mathematics, including Kac-Moody algebras, the Yang-Baxter equation, q-series, Painlevé equations, and conformal field theory. Zamolodchikov's amazing discovery was that the conformal field theory that describes the model at its critical point can remain integrable when one perturbs away from the critical point in certain directions. One of these perturbations corresponds physically to turning on an external magnetic field. It is in this context that the $E_8$ symmetry emerges.

Since the Ising model is a toy model - real ferromagnets are messier (and 3-dimensional!) - it doesn't really need experimental test. The model is important more for the physical and mathematical insight it gives, than for any quantitative information it might yield. Nevertheless, there is a tradition of trying to find real physical systems that embody the simple microscopic picture of the Ising model. (Such systems have to behave effectively as if they are one or two dimensional.) The recent work lies within this tradition, and they have managed to verify one of the consequences of Zamolodchikov's work, namely that the mass ratio of the two lightest quasiparticles is $\phi$. I have no reason to doubt that what Coldea et al. measured in their experiment is a genuine manifestation of the $E_8$ symmetry of the model.

One consequence of the $E_8$ symmetry is that there are eight species of particles, with definite mass ratios. If I had to guess, I would say that it's going to be very difficult to observe the peaks corresponding to the remaining particles. The third particle has a mass very close to twice that of the lightest particle, which means that that peak will be buried under lots of nearby two-particle states. Furthermore, the particles with masses higher than two will be unstable. (The field theory studied by Zamolodchikov is integrable and therefore does not have unstable particles, but any attempt to realize the model experimentally will surely destroy the integrability and therefore the stability of the higher-mass particles.)

Note: The one-dimensional quantum spin chain model in the Science article is described by a Hamiltonian that has the same eigenvectors as the transfer matrices of the classical two-dimensional square lattice Ising model solved by Onsager. So for the purposes of this discussion they are equivalent.

**Addendum:** (This an answer to the comment of Victor Prostak that was too large to fit in the comment box.) It is widely believed (but not a theorem as far as I know) that there are only two integrable perturbations: Onsager's thermal perturbation, which has a very simple symmetry, and Zamolodchikov's magnetic perturbation with the $E_8$ symmetry. The model is not expected to be integrable if one does both perturbations simultaneously, but the question is physically just as interesting, and was studied in B.M. McCoy and T.T. Wu, Two-dimensional Ising field theory in a magnetic field: Breakup of the cut in the two-point function, *Phys. Rev. D* **18**, 1259–1267 (1978). I am not aware of any computation of the mass ratios in the general case. I wouldn't expect any exceptional symmetries to show up.

On the other hand, exceptional groups do show up in related conformal field theories. A perturbation of the $\mathcal{M}(4,5)$ minimal model with central charge $c=7/10$ has an $E_7$ symmetry, and a perturbation of the $\mathcal{M}(6,7)$ minimal model with central charge $c=6/7$ has an $E_6$ symmetry. These models describe different kinds of critical points than the $c=1/2$ model does, and so are experimentally distinguishable. In addition, the mass ratios of the quasiparticles should be different.

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