Non-equilibrium gelation transition in a kinetic lattice gas model

– We consider a lattice gas model which in addition to the canonical nearest neighbor pair interatomic interaction accounts for a many-body interaction inside atomic trios. Interactions of this kind arise in the coherent strained epitaxy and were recently used by us to describe some surface phenomena. With the use of the Monte Carlo simulation we show that in two dimensions the model at low temperature exhibits glassy behaviour, in particular, undergoes a gelation transition. We argue that this model may belong to the universality class of non-equilibrium critical phenomena which may comprise also some off-lattice structural glass transitions, provided such a class exists. It seems to be firmly established that the glass transition which has been the subject of extensive study in recent years (see review papers [1,2,3]) does not belong to the category of the familiar equilibrium phase transitions but is a purely kinetic phenomenon which occurs in some many-body far from equilibrium systems (FFES) [1]. Thus, our poor understanding of glassy phenomena [4, 2] can be related to the poor development of the non-equilibrium statistical physics in comparison with its equilibrium counterpart. Historically, investigation of the non-equilibrium kinetics went in parallel with the equilibrium studies () but only for systems in the vicinity of equilibrium a systematic approach based on the linear response theory has been developed [5] while in the far from equilibrium case any technique of comparable generality is absent. A major difficulty in developing a unified description of the FFES is their much larger diversity in comparison with the near-equilibrium ones () and that some of them are very complex, biological systems being the standard example. So it seems unrealistic to expect that a microscopic approach similar to LRT can be built which would be equally applicable to all FFES. Therefore, alongside with microscopic theories of individual FFES, phenomenological ()The famous Boltzmann equation (1872) appeared practically simultaneously with the modern formulation of the laws of thermodynamics. ()While near equilibrium systems in statistical terms can be considered as linear perturbations in the vicinity of a canonical equilibrium ensemble, the FFES comprise all other statistical ensembles.