#### IMSc Webinar

#### Entropy-driven phase transitions in hard core lattice gas models in three dimensions

#### N. Vigneshwar

##### IMSc

*There are a class of phase transitions where the transition to the ordered state is driven by a gain in entropy. These transitions are manifested in experimental systems like freezing in hard-spheres of PMMA colloids, nematic transitions in liquid crystals, etc. The minimal models for studying these transitions are volume exclusion models, In such systems, all allowed configurations have equal energy, and therefore any phase transitions are driven purely by gain in entropy. When placed on lattices, these models are called hard-core lattice gas models. These models serve as nice abstraction for actual experimental systems and understanding their phase diagram on lattice is helpful in general understanding of entropy-driven phase transitions. Various shapes have been studied on many two-dimensional lattices using approximate theories and numerical simulations. In three-dimensions, it is more complicated to study them because of the lack of efficient algorithms to simulate such systems at high densities or large exclusion volumes. Here we study two problems on a cubic lattice: (1) hard rods of length k and (2) hard cubes of size 2 × 2 × 2. We obtain the detailed phase diagram and characterize the nature of the phase transitions for both these models.*

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