What is the second order phase transition?
During a second-order phase transition, the order parameter is equal to zero above and at the transition point. Similar behavior is exhibited by, for example, the magnetic dipole moment of a ferromagnet, the electric polarization of a ferroelectric, the density of the superfluid component in liquid 4 He, and the probability of finding an A atom at the appropriate lattice point of a binary alloy.
As you explained, the first case, the entropy suddenly jumps (the pieces suddenly curved), it means the phase transition is first order, while in second case, the entropy continuously increase (C.
An example for a second order transition is the conducting-superconducting transition in metals at low temperatures. Other types of second order transitions are solid-solid (structural) transition in crystals.
Second-order Phase transitions. In a second-order phase transition, the first derivative of the slope of m is not discontinuous but it's second derivative is. In other words, there is an inflection point at the phase transition. This type of transitions occurs between conducting and superconducting phases of metals at low temperatures. l.
Charge ordering (CO) is a (first- or second-order) phase transition occurring mostly in strongly correlated materials such as transition metal oxides or organic conductors.Due to the strong interaction between electrons, charges are localized on different sites leading to a disproportionation and an ordered superlattice.It appears in different patterns ranging from vertical to horizontal.
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The non-analyticity at a phase transition then comes because in the partition function one must sum over all possible values of the order parameter. Landau’s theory of phase transitions is based on an expansion of the free energy of a thermodynamic system in terms of an order parameter, which is nonzero in an ordered phase and zero in a disordered phase.