Thermal negativity in a two qubit XXX and XX spin chain model in an external magnetic field

In this paper we studied the thermal negativity in a two-qubit XX spin ½ chain model and XXX spin 1/2 chain model(isotropic Heisenberg model)spin-1/2 chain subjected to an external magnetic field in z direction. We calculate analytical relation for the thermal negativity for two qubit XX and XXX spin chain models in the external magnetic field. Effects of the magnetic field and temperature on the negativity are shown. We have also plotted two kind of behavior in the thermal negativity which scales by magnetic field and temperature. It is shown that when the magnetic field along in axis z is considerable, thermal negativity can be decrease for higher temperature. We found the critical temperature of negativity for XX spin chain model and XXX spin chain model with added external magnetic field where there are independent from magnetic field. We also have shown in both of two models after T=TC the negativity is zero. We find the critical temperature for this models and show that the critical temperature is independent of magnetic field. We found that the negativity with increasing the temperature T, at first the quantum correlations in the system increase, smoothly reaches the maximum, and then after the critical temperature turn into zero.