A glass of solidified glass may seem motionless, but inside, the atoms are frozen in random positions, never having found perfect order. A similar situation occurs in spin glasses: the magnetic moments of atoms freeze, pointing in different directions, and the material loses the ability to be simply magnetized.
When you turn on an external magnetic field, the picture becomes more complicated. In an ordinary magnet, all moments align with the field, but in a spin glass, some moments resist because random interactions with neighbors hold them back. The question is whether the system remains 'frozen' or gradually rearranges. Physicists have proposed several scenarios, and the debate has lasted half a century. The new computational method proposed by the authors allows measuring susceptibility, how readily the material responds to the field, even when standard approaches fail due to broad tails in the overlap distribution.
Computer simulations revealed a striking difference. For the standard Ising model and the two-dimensional spin glass, the line of susceptibility maxima in the field–temperature plane bends to the right — a sign of a supercritical crossover line, a smooth transition without a sharp boundary. But for the three-dimensional spin glass and the mean-field model, the line bends to the left: that is the de Almeida–Thouless line, a genuine phase transition. Further finite-size analysis showed that in the three-dimensional case, the susceptibility peak grows with system size, while in the two-dimensional case, it saturates.
This result is the first direct numerical evidence of the de Almeida–Thouless transition in a three-dimensional spin glass. It supports the replica symmetry breaking scenario, one of the most elegant and controversial ideas in statistical physics. The glass of glass turned out to be not so simple: under a field, it doesn't just 'heat up,' but passes through a special point where its internal disorder changes its nature.
The de Almeida–Thouless line is named after two physicists who predicted its existence in 1978 using an elegant mathematical trick, but until now no one had been able to confirm it numerically in a three-dimensional model.