# Does one-dimensional ferromagnetic chain have long range order at zero tempreture?

In many text books on one dimensional quantum magnetic systems, it's said there is no orderd state for one dimensional magnetic systems. I understand that the one dimensional spin half Antiferromagnetic chain has no truly long range order since its correlation function decays exponentially at large distance. How about the ferromagnetic chain, especially when all the spins are in the same up state?
Ferromagnetic chain or Ising chain with transverse field has ordered states at zero tempreture. There is also other ordered states proved to be exist when T=0, such as the off-diagnol long range order(https://journals.aps.org/prb/cited-by/10.1103/PhysRevB.47.1113). So I think the text books I mention only meant for the disorderd chains, such as antiferromagnetic chain.