Square Ising model with second-neighbor interactions and the Ising chain in a transverse field.

Abstract

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.