The square Ising model with second-neighbor interactions and the Ising chain in a transverse field

Pierre M. Pfeuty

Marcelo D. Grynberg, B. Tanatar

We consider the thermal and critical behavior of the square Ising lattice with frustrated first- and second-neighbor interactions. A low-temperature domain-wall analysis including kinks and dislocations shows that there is a close relation between this classical model and the Hamiltonian of an Ising chain in a transverse field provided that the ratio of the next-nearest--to--nearest-neighbor coupling is close to 1/2. Due to the field-inversion symmetry of the Ising-chain Hamiltonian, the thermal properties of the classical system are symmetrical with respect to this coupling ratio. In the neighborhood of this regime critical exponents of the model turn out to belong to the Ising universality class. Our results are compared with previous Monte Carlo simulations.

Michael W. Klein, Zhong He Wang

We consider an infinite chain of four-orientational hindered dipoles with near-neighbor interaction J. The dipoles are allowed to undergo tunneling into the near-neighbor wells (90\ifmmode^\circ\else\textdegree\fi{} tunneling) on the same site. We show that the partition function ${Z}_{D}$(J) of the dipoles is ${Z}_{D}$(J)=${Z}_{S}^{2}$(J/2), where ${Z}_{S}$ is the partition function for a chain of Ising-model spins in a transverse field similar to that treated by Pfeuty. The dipoles act like a pair of independently embedded Ising-spin chains in a transverse field.

Amir Hajibabaei, Farhad Shahbazi

In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustrating second neighbor coupling ( k<0.4 ), the exponents are the same as those of the classical 2D Ising model (B=1/8 and Y=7/8), but a deviation from 2D classical Ising universality class is observed for larger values of frustration (0.4< K<0.5). The reason for this deviation is the “disorder line” which becomes tangent to the Ferromagnetic phase boundary line at K=0.5

Subir Sachdev A