Elasticity and metastability limit in supercooled liquids: a lattice model

Abstract

We present Monte Carlo simulations on a lattice system that displays a first-order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models. The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.

Acknowledgments

We thank C. Di Castro and J. Dyre for many useful comments and clarifying discussions.

Notes

†For every site we define m_i in this way. First we set m _i =0 for all sites. Then the sites are considered sequentially. If the spin is σ _i =−1 and it is surrounded by four spins whose values are +1, we increase m _i by 1 for each of these five sites. One can check that with this definition the ground state found in 3 has m _i =1 for every site, while in the liquid phase m _i has, on average, a small value.

† In some configurations m _i can be larger than 1 but these configurations are very rare.

†One may define more than one relaxation time, as studied in 4, but here we refer to the higher value taken by these relaxation times.

†We thank Jeppe Dyre for helping us improve our theory regarding this point. The details of this calculation will be published elsewhere.