A ferromagnet with a glass transition

– We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one-step replica-symmetry–broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level. Over the last decades there has been a growing interest in understanding the structural glass transition in complex materials. A major theoretical role has been played by mean-field theories based on fully connected p-spin-glass models [1–3]. In such models, it was possible to identify a purely dynamical transition which accounts for the off-equilibrium behaviour of the models, and which is believed to present some analogies to the structural glass transition in realistic systems [4–7]. Although this analogy is very fruitful, one must keep in mind that the mean-field spin-glass models which have been considered are rather remote from the structural glasses. Let us mention just the three most obvious differences: they have no crystalline state, their Hamiltonian has quenched-in disorder, in the form of an extensive number of quenched coupling constants, and these couplings are of infinite range. A lot of work has already been devoted to cure these defects, in order to get a much closer analogy between some lattice spin models and structural (∗) E-mail: [email protected] (∗∗) E-mail: [email protected] (∗∗∗) E-mail: [email protected] (∗∗∗) E-mail: [email protected] (∗∗∗) E-mail: [email protected]