I'm studying the 2D Ising model and saw a solution, that first formalized it by using a transfer matrix $T$ and then by the identification $T = e^{-\hat{H}\Delta t}$ as $H = -\sum_a \sigma_a^{x}+ \lambda\sigma_a^z\sigma_{a+1}^z$. This Hamiltonian seems to me to have the same form of the transverse field Ising model. Though I did a lot of research, I couldn't verify it anywhere. Could you explain to me if my observation is correct (that the 2D Ising model corresponds to the transverse field 1D Ising chain) or give me a reference?
The Ansatz with the transfer matrix I got from this paper https://academic.oup.com/book/43943/chapter-abstract/368950100?redirectedFrom=fulltext