Editing Landau theory of phase transitions
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In the '''Landau theory of phase transitions''' of [[Lev Davidovich Landau]] | In the '''Landau theory of phase transitions''' of [[Lev Davidovich Landau]], the [[thermodynamic potential]] takes the form of a [[power series]] in the [[order parameters |order parameter]] (<math>\eta</math>) (Ref. 3 Eq. 143.1) | ||
:<math>\left.\Phi(p, T, \eta)\right. = \Phi_0 + \alpha(p,T)\eta + A(p,T)\eta^2 + | :<math>\left.\Phi(p, T, \eta)\right. = \Phi_0 + \alpha(p,T)\eta + A(p,T)\eta^2 + B(p,T)\eta^3 + C(p,T)\eta^4 + ...,</math> | ||
where <math>p</math> is the [[pressure]] and <math>T</math> is the [[temperature]]. | |||
The the equilibrium state consistent with the external parameters <math>p</math> and <math>T</math> is a minimum of the Landau potential (often also called Landau free energy). This yields a prescription for determining the equilibrium value adopted by <math>\eta</math> | The the equilibrium state consistent with the external parameters <math>p</math> and <math>T</math> is a minimum of the Landau potential (often also called Landau free energy). This yields a prescription for determining the equilibrium value adopted by <math>\eta</math> | ||
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The Landau theory is phenomenological in nature. Nothing is known a priori about the coefficients of the series. Whereas this is a strong point in order to highlight universal features, it is clear that any useful assumption about the symmetry or vanishing of such coefficients requires a fair understanding of the transition beforehand | The Landau theory is phenomenological in nature. Nothing is known a priori about the coefficients of the series. Whereas this is a strong point in order to highlight universal features, it is clear that any useful assumption about the symmetry or vanishing of such coefficients requires a fair understanding of the transition beforehand | ||
==References== | ==References== | ||
#Lev Davidovich Landau "", Physikalische Zeitschrift der Sowjetunion '''11''' pp. 26-47 (1937) | |||
#Lev Davidovich Landau "", Physikalische Zeitschrift der Sowjetunion '''11''' pp. 545-555 (1937) | |||
#L. D. Landau and E. M. Lifshitz, "Statistical Physics" (Course of Theoretical Physics, Volume 5) 3rd Edition Part 1, Chapter XIV, Pergamon Press (1980) | |||
#[http://dx.doi.org/10.1088/0022-3719/9/9/015 A P Cracknell, J Lorenc and J A Przystawa "Landau's theory of second-order phase transitions and its application to ferromagnetism", Journal of Physics C: Solid State Physics '''9''' pp. 1731-1758 (1976)] | |||
[[category: classical thermodynamics]] | [[category: classical thermodynamics]] |