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Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. [6]
Landau theory (also known as Ginzburg–Landau theory, despite the confusing name [1]) in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. [2]
These continuous transitions from an ordered to a disordered phase are described by an order parameter, which is zero in the disordered and nonzero in the ordered phase. For the aforementioned ferromagnetic transition, the order parameter would represent the total magnetization of the system.
Those lines are high-symmetry residuals within the symmetry broken phase. It is characteristic for a continuous phase transition that the energy difference between ordered and disordered phase disappears at the transition point. This implies that fluctuations between both phases will become arbitrarily large.
Mathematically, a phase transition occurs when the partition function vanishes and the free energy is singular (non-analytic). For instance, if the first derivative of the free energy with respect to the control parameter is non-continuous, a jump may occur in the average value of the fluctuating conjugate variable, such as the magnetization ...
A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero.A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping.
The Berezinskii–Kosterlitz–Thouless (BKT) transition is a phase transition of the two-dimensional (2-D) XY model in statistical physics.It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature.
Continuous phase transitions (critical points) of classical statistical physics systems with D spatial dimensions are often described by Euclidean conformal field theories. A necessary condition for this to happen is that the critical point should be invariant under spatial rotations and translations.