Simple lattice models of complex systems

Abstract

Collective phenomena in systems containing particles that self-assemble into different non-homogeneous structures exhibit similar properties, despite different physical origins 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 are described. The models include: (i) simple cubic lattice model for water, predicting all major anomalies, (ii) simple lattice model for polar molecules (methanol) predicting orientational ordering of molecules into zig-zag chain-like clusters and (iii) 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.