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 spin1/2 chain model(isotropic heisenberg model)spin-1/2 chain subjected to an external magnetic field inz direction. we calculate analytical relation for the thermal negativity for two qubit xx and xxx spinchain models in the external magnetic field. effects of the magnetic field and temperature on thenegativity are shown. we have also plotted two kind of behavior in the thermal negativity whichscales by magnetic field and temperature. it is shown that when the magnetic field along in axis z isconsiderable, thermal negativity can be decrease for higher temperature. we found the criticaltemperature of negativity for xx spin chain model and xxx spin chain model with added externalmagnetic field where there are independent from magnetic field. we also have shown in both of twomodels after t=tc the negativity is zero. we find the critical temperature for this models and showthat the critical temperature is independent of magnetic field. we found that the negativity withincreasing the temperature t, at first the quantum correlations in the system increase, smoothlyreaches the maximum, and then after the critical temperature turn into zero.