STAT In the literature: contested

Replica symmetry breaking or droplets in the 3D Edwards-Anderson model

In plain words

Below its freezing temperature, does a three-dimensional spin glass have many distinct frozen states, as in the solvable infinite-range model, or essentially one state and its mirror image? The two pictures predict different responses to small changes in temperature or magnetic field.

Precise statement

For the 3D Edwards-Anderson Ising model H = -sum_<ij> J_ij s_i s_j with symmetric Gaussian or $\pm J$ couplings at $T < T_c$, determine in the thermodynamic limit whether the spin overlap distribution $P(q)$ keeps a continuous part between $-q_{\mathrm{EA}}$ and $q_{\mathrm{EA}}$ (replica symmetry breaking, RSB), whether system-spanning excitations cost $O(1)$ energy (RSB) or grow as $L^{\theta}$ with $\theta > 0$ (droplet picture), or whether the intermediate trivial-nontrivial (TNT) scenario holds. An answer is one of these classifications supported by finite-size analysis that controls the $L \to \infty$ limit, or by a proof.

What would settle it

Equilibrium simulations or ground-state computations at sizes large enough to fix the L dependence of P(q) and of domain-wall and sponge excitation energies without ambiguity.

Status in the literature

Simulations at accessible sizes look RSB-like, while droplet proponents argue these sizes are preasymptotic (M. A. Moore, arXiv:2103.02973, 2021).