Volcano transition in a solvable model of oscillator glass

In 1992 a puzzling transition was discovered in simulations of randomly coupled limit-cycle oscillators. This so-called volcano transition has resisted analysis ever since. It was originally conjectured to mark the emergence of an oscillator glass, but here we show it need not. We introduce and solve a simpler model with a qualitatively identical volcano transition and find, unexpectedly, that its supercritical state is not glassy. We discuss the implications for the original model and suggest experimental systems in which a volcano transition and oscillator glass may appear.