Lattice systems are a type of mathematical model used to study the behavior of physical systems, such as crystals, polymers, or magnetic materials. In a lattice system, particles or sites are arranged in a regular, repeating pattern in one, two, or three dimensions. The interactions between these particles are typically represented by a mathematical function, which describes how they influence each other's behavior. Researchers use lattice systems to study phenomena such as phase transitions, magnetic ordering, and the propagation of waves through a material. By studying these systems, scientists can gain insight into the underlying principles that govern the behavior of complex materials and better understand their properties. Overall, lattice systems provide a useful framework for studying the behavior of physical systems at a microscopic level, allowing researchers to make predictions about their macroscopic behavior.