Equation of state and quantal crossover of the XY model in a longitudinal magnetic field

K. Lukierska‐Walasek

K. Lukierska‐Walasek

Takashi Tonegawa

K. Lukierska‐Walasek

The equation of state of the transverse Ising model in a longitudinal field B is investigated in the vicinity of the zero-temperature multicritical point by using the renormalisation group method recently proposed by the author and K. Walasek (1983). For the critical value of transverse field the scaling crossover form of the relation between the longitudinal magnetic field and magnetisation M is obtained as B approximately M delta q Psi (z) with z approximately TM - phi beta q/, where phi , delta q and beta q denote the crossover and multicritical exponents. The crossover scaling function Psi (z) is calculated for the spatial dimensions d<or=3 and 3<d<4 to the first order in epsilon '=3-d and epsilon =4-d, respectively.

Naoki Suzuki, Fumitaka Matsubara

We study the S= quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins N\ensuremath{\leqslant}27, and those at finite temperatures using a quantum transfer Monte Carlo method for N\ensuremath{\leqslant}24. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3 plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic-field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin-flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.

H. Arefazar, Mohammad Reza Soltani

We have examined the effect of a DM interaction and longitudinal external magnetic field on the energy gap of a two-qubit spin-1/2 XY mode. Also we have calculated the critical values of DM interaction and longitudinal external magnetic field. We have shown that DM interaction and external magnetic field have an effect on the energy gap behavior and critical values and also we have been able to get phase transition point