Simple lattice models of complex systems
Alina Ciach
Collective phenomena in systems containing particles that self-assemble into different non-homogeneous structures exhibit similar properties, despite different physical origin of interactions. Universal properties of a class of such systems can be described by highly simplified models that capture key properties of the (effective) interactions. Phase transitions and structural properties for a few such generic models will be described. The models include:(i) a triangular lattice model for particles that interact with short-range attraction and long-range repulsion potential (SALR), and are adsorbed on different surfaces; this can be a toy model for protein rafts on biological membranes, since 'rafts' and 'stripes' correspond to thermodynamically stable structures in different conditions (ii) simple cubic lattice model for water, predicting all major anomalies and (iii) simple lattice model for alcohol (polar molecules) predicting orientational ordering of molecules into zig-zag chain-like clusters.