Solving the one-dimensional Ising chain via mathematical induction: An intuitive approach to the transfer matrix
Abstract
The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalized to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be of broad interest for undergraduate teaching in statistical mechanics.
Keywords
Cite
@article{arxiv.1907.11701,
title = {Solving the one-dimensional Ising chain via mathematical induction: An intuitive approach to the transfer matrix},
author = {Wenlong Wang and Rogelio Díaz-Méndez and Raudys Capdevila},
journal= {arXiv preprint arXiv:1907.11701},
year = {2020}
}
Comments
6 pages, 1 figure