It is amazing, that in the 2D Ising model transition between these two phases is remarkably sharp, since M approches zero at critical temperature T_{c} = 2.2692... with infinite slope. This phenomenon is called the second order phase transition. In this transition order parameter M is continuous but susceptibility c and specific heat C, which are expressed as the second derivatives of the partition function Z, diverge at T_{c} . Order parameter is expressed as the first derivative of Z and it is discontinuos at the critical temperature in the first order phase transition. |
H.Eugene Stanley "Scaling, universality, and renormalization"
Rev.Mod.Phys. 71, S359 (1999).
D.P.Landau "Finite-size behavior of the Ising square lattice"
Phys.Rev.B 13, 2997 (1976).