Spin Glass Models of Syntax and Language Evolution

Using the SSWL database of syntactic parameters of world languages, and the MIT Media Lab data on language interactions, we construct a spin glass model of language evolution. We treat binary syntactic parameters as spin states, with languages as vertices of a graph, and assigned interaction energies along the edges. We study a rough model of syntax evolution, under the assumption that a strong interaction energy tends to cause parameters to align, as in the case of ferromagnetic materials. We also study how the spin glass model needs to be modified to account for entailment relations between syntactic parameters. This modification leads naturally to a generalization of Potts models with external magnetic field, which consists of a coupling at the vertices of an Ising model and a Potts model with q=3, that have the same edge interactions. We describe the results of simulations of the dynamics of these models, in different temperature and energy regimes. We discuss the linguistic interpretation of the parameters of the physical model.
Comment: 19 pages, LaTeX, 20 png figures