Ground states of one-dimensional antiferromagnetic models with long-range interaction

Azer Kerimov

Sibin Yang, Dao‐Xin Yao, Anders W. Sandvik

Biao Hao, Chang-De Gong

J. Rodrigo Parreira, Oscar Bolina, J Fernando Perez

We consider the ground state of one-dimensional antiferromagnets with long-range interactions with Hamiltonian given by where , with J>0. We prove Néel order for all if the spin s is sufficiently large. We also prove the absence of long-range order when for any spin value.

Alessandro Giuliani, Joel L. Lebowitz, Élliott H. Lieb

We study the ground state of a $d$-dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The long-range interaction is equal to ${r}^{\ensuremath{-}p}$, $p>d$, while the FM interaction has strength $J$. If $p>d+1$ and $J$ is large enough the ground state is FM, while if $d<p\ensuremath{\leqslant}d+1$ the FM state is not the ground state for any choice of $J$. In $d=1$ we show that for any $p>1$ the ground state has a series of transitions from an antiferromagnetic state of period 2 to $2h$-periodic states of blocks of sizes $h$ with alternating sign, the size $h$ growing when the FM interaction strength $J$ is increased (a generalization of this result to the case $0<p\ensuremath{\leqslant}1$ is also discussed). In $d\ensuremath{\geqslant}2$ we prove, for $d<p\ensuremath{\leqslant}d+1$, that the dominant asymptotic behavior of the ground-state energy agrees for large $J$ with that obtained from a periodic striped state conjectured to be the true ground state. The geometry of contours in the ground state is discussed.

Subir Sachdev A, Kwon Park