Symmetries and Dynamics of Discrete Systems

TL;DR

This paper explores the symmetry properties of discrete dynamical systems and lattice models, introducing a C program for symmetry analysis, phase portrait construction, and phase transition detection, with applications to soliton-like structures.

Contribution

It presents a novel computational tool for symmetry analysis and dynamic investigation of discrete systems, including phase portraits and phase transition detection.

Findings

Identification of symmetry groups in discrete systems

Construction of phase portraits modulo symmetries

Observation of soliton-like structures in cellular automata

Abstract

We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program constructs and investigates phase portraits of discrete dynamical systems modulo groups of their symmetries, searches dynamical systems possessing specific properties, e.g., reversibility, computes microcanonical partition functions and searches phase transitions in mesoscopic systems. Some computational results and observations are presented. In particular, we explain formation of moving soliton-like structures similar to ``spaceships'' in cellular automata.