Transfer Matrix of the Two-dimensional Ising Model

Giuseppe Mussardo

Published Mar 26, 2020• 0 citations

Abstract

Abstract This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

DOI: 10.1093/oso/9780198788102.003.0006

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