Calculation of critical exponents in two dimensions from quantum field theory in one dimension

TLDR: In this paper, a relationship between the Baxter model in two dimensions and the Luttinger model in one was constructed, and the relationship was used to calculate critical exponents for the Baxter models from appropriate Lutteringer-model correlation functions.

Abstract: We construct a relationship between the Baxter model in two dimensions and the Luttinger model in one, and use it to calculate critical exponents for the Baxter model from appropriate Luttinger-model correlation functions. An important part of this work involves the generalization of the Jordan-Wigner transformation to provide a representation for continuum spin operators. With this generalization, we are also able to calculate spin correlation functions for a continuum generalization of the spin-\textonehalf{} Heisenberg-Ising chain. We discuss the difference between the continuum and discrete lattice models, and with the help of a new scaling law, use previous results for the Baxter model to calculate new exponents for the Baxter and Heisenberg-Ising model on a lattice.