What Is a Pattern in Statistical Mechanics? Formalizing Structure and Patterns in One-Dimensional Spin Lattice Models with Computational Mechanics (opens in new tab)

This work formalizes the notions of structure and pattern for three distinct one-dimensional spin-lattice models (finite-range Ising, solid-on-solid, and three-body), using information-theoretic and computation-theoretic methods. We begin by presenting a novel derivation of the Boltzmann distribution for finite one-dimensional spin configurations embedded in infinite ones. We next recast this distribution as a stochastic process, thereby enablin...