It is the temperature in which the staggered magnetization (= a measure on how much nearest neighbors tend to align oppositely) is nonzero. The magnetization is both zero for a paramagnet and an antiferromagnet.
Can I say for [tex]\sigma=0[/tex], [tex]T=T_N[/tex]?
What do you mean by sigma=0? If you mean that the entropy is zero, I don't think so. It holds when all the local moments are 'fully' aligned(such that two nearest neighbors point in opposite directions). At the Neel temperature, such alignment starts to develop.