Alladi Ramakrishnan Hall

Entropy driven phase transitions in hard core lattice gases (Pre-synopsis seminar)

Dipanjan Mandal

Institute of Mathematical Sciences

Entropy driven phase transitions are often observed in nature. Examples include freezing transition in a system of hard spheres, disordered-nematic-smectic transition in a system of long rods, ordering transition in adsorbed layers of gases on metallic surface, etc. Hard core lattice gas models, where particles constrained to lattices interact only through excluded volume interactions, are minimal models to study entropy-driven phase transitions. The emergent phases and the different phase transitions depend only on the shape and density of the particles, as the temperature does not play any role. Despite a long history of study, it is not understood what the precise dependence between the shapes of the particles and the emergent phases is, even more so in three dimensions.

In this talk, I will discuss in detail the phase diagram of four models of differently shaped particles both in two and three dimensions. These are which are (a) 2 X 2 hard squares, (b) mixture of 2 X 1 dimers and 2 X 2 squares on a square lattice, (c) 2 X 2 X 1 hard plates on a cubic lattice and  (d) Y-shaped particles on a triangular lattice. Each of these models are motivated from physical examples, which will I will elaborate on. Using both analytical techniques and large-scale Monte Carlo simulations the phase diagram of the models are obtained. The nature of the phase transitions are characterised in detail.