High order perturbation study of the frustrated quantum Ising chain

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