One-dimensional inhomogeneous Ising model: A new approach

Jerome K. Percus, M. Q. Zhang

In this paper, we focus on the essential difference between the inhomogeneous one-dimensional Ising model with open and periodic boundary conditions. We show that, although the profile equation in the periodic case becomes highly nonlocal, due to a topological collective mode, there exists a local free-energy functional in an extended space and one can solve the inhomogeneous problem exactly.

Louis J. Kijewski, M. P. Kawatra

John R. Hamm

Shahane A. Khachatryan, Hrachia Babujian, A. Sedrakyan

We investigate a generalized inhomogeneous two-dimensional Ising model on the kagomé lattice with two alternating couplings J i and J i ′ , i = 1 , 2 , 3 , along the three lattice directions. The local Boltzmann weights are mapped onto a non-symmetric eight-vertex R -matrix satisfying the free-fermion condition for arbitrary values of the six couplings. We analyze the Yang–Baxter structure for the cases J i ′ = J i and J i ′ = − J i and derive the corresponding one-dimensional quantum spin chains in the anisotropic limit. The first case yields a transverse-field Ising-type Hamiltonian, while the second leads to a modified chain with a graded permutation structure and shifted partition-function zeros. For a partially anisotropic model, we also obtain the free energy and specific heat.

Shahane A. Khachatryan, Hrachya M. Babujian, A. Sedrakyan

We investigate a generalized inhomogeneous two-dimensional Ising model on the kagomé lattice with two alternating couplings $J_i$ and $J'_i$, $i=1,2,3$, along the three lattice directions. The local Boltzmann weights are mapped onto a non-symmetric eight-vertex $R$-matrix satisfying the free-fermion condition for arbitrary values of the six couplings. We analyze the Yang--Baxter structure for the cases $J'_i=J_i$ and $J'_i=-J_i$ and derive the corresponding one-dimensional quantum spin chains in the anisotropic limit. The first case yields a transverse-field Ising-type Hamiltonian, while the second leads to a modified chain with a graded permutation structure and shifted partition-function zeros. For a partially anisotropic model, we also obtain the free energy and specific heat.

A.P. Vieira, L.L. Gonçalves