Magnetic properties of the 1D mixed spin-1/2 and spin-S (S >1/2) transverse Ising model in the presence of an external longitudinal magnetic field are calculated exactly by the use of the generalised decoration-iteration mapping transformation. By assuming that only the spin-S atoms do interact with the transverse field the exact results for the Gibbs free energy, longitudinal magnetization, transverse magnetization, entropy and specific heat have been derived and discussed in detail. In addition to the standard temperature variations of the transverse magnetization, another two non-trivial thermal dependences have been found. The results support the concept that the spin reorientation from the longitudinal towards the transverse field direction takes place in the narrow temperature region.Magnetic properties of the 1D mixed spin-1/2 and spin-S (S >1/2) transverse Ising model in the presence of an external longitudinal magnetic field are calculated exactly by the use of the generalised decoration-iteration mapping transformation. By assuming that only the spin-S atoms do interact with the transverse field the exact results for the Gibbs free energy, longitudinal magnetization, transverse magnetization, entropy and specific heat have been derived and discussed in detail. In addition to the standard temperature variations of the transverse magnetization, another two non-trivial thermal dependences have been found. The results support the concept that the spin reorientation from the longitudinal towards the transverse field direction takes place in the narrow temperature region.

arXiv:cond-mat/0207518Jul 22, 20020 citations

Simulating an exact one-dimensional transverse Ising model in an optical lattice

Ren Liao, Fangyu Xiong, Xuzong Chen

A spinless Bose-Hubbard model in a one-dimensional (1D) double-chain tilted lattice is numerically studied at unit filling per cell. When each atom is localized in a two-site cell, the low-energy effective model gives rise to an exact textbook model of the 1D transverse Ising model via superexchange interaction. To validate the effective transverse Ising model, we calculate the energy spectrum and the nearest-neighbor correlation functions of the states in a subspace of the Bose-Hubbard model which is equivalent to the Hilbert space of a spin-1/2 magnetic model. The results show good consistency with the effective transverse Ising model, and we show that it is possible to simulate the dynamical quantum phase transition of the 1D transverse Ising model exactly with such a double-chain Bose-Hubbard model. Our results may provide some inspirations for realizing and exploring an exact 1D transverse Ising model in ultracold neutral atom systems.A spinless Bose-Hubbard model in a one-dimensional (1D) double-chain tilted lattice is numerically studied at unit filling per cell. When each atom is localized in a two-site cell, the low-energy effective model gives rise to an exact textbook model of the 1D transverse Ising model via superexchange interaction. To validate the effective transverse Ising model, we calculate the energy spectrum and the nearest-neighbor correlation functions of the states in a subspace of the Bose-Hubbard model which is equivalent to the Hilbert space of a spin-1/2 magnetic model. The results show good consistency with the effective transverse Ising model, and we show that it is possible to simulate the dynamical quantum phase transition of the 1D transverse Ising model exactly with such a double-chain Bose-Hubbard model. Our results may provide some inspirations for realizing and exploring an exact 1D transverse Ising model in ultracold neutral atom systems.

arXiv:2003.02411Physical Review AApr 8, 202115 citations

Some Exact Results for Multiorientational "Ising-Type" Dipoles in Transverse Fields

Michael W. Klein, Zhong He Wang

We consider a system of ${2}^{n}$ orientational interacting tunneling dipoles in $n$ transverse near-neighbor-well tunneling fields $^{\ensuremath{\alpha}}\ensuremath{\Delta}$ ($1>~\ensuremath{\alpha}>~n$). We show that the partition function for the system can be expressed as a product of $n$ Ising-model partition functions in transverse fields. The results are valid in one, two, and three dimensions as well as for random $\ensuremath{\Delta}$ s and random general interaction potentials.We consider a system of ${2}^{n}$ orientational interacting tunneling dipoles in $n$ transverse near-neighbor-well tunneling fields $^{\ensuremath{\alpha}}\ensuremath{\Delta}$ ($1>~\ensuremath{\alpha}>~n$). We show that the partition function for the system can be expressed as a product of $n$ Ising-model partition functions in transverse fields. The results are valid in one, two, and three dimensions as well as for random $\ensuremath{\Delta}$ s and random general interaction potentials.

Physical Review LettersSep 15, 19868 citations

The one dimensional Ising model with a transverse field

Annals of PhysicsFeb 1, 197063 citations

We consider a system of

{2}^{n}

orientational interacting tunneling dipoles in

n

transverse near-neighbor-well tunneling fields $^{\ensuremath{\alpha}}\ensuremath{\Delta}$ ($1>~\ensuremath{\alpha}>~n$). We show that the partition function for the system can be expressed as a product of

n

Ising-model partition functions in transverse fields. The results are valid in one, two, and three dimensions as well as for random $\ensuremath{\Delta}$ s and random general interaction potentials.