By Julio A. Gonzalo

ISBN-10: 9812568751

ISBN-13: 9789812568755

ISBN-10: 9812773126

ISBN-13: 9789812773128

This booklet starts through introducing the powerful box process, the best method of section transitions. It presents an intuitive approximation to the physics of such different phenomena as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity. the relationship among the potent box process and Landau's idea is under pressure. the most assurance is dedicated to precise functions of the powerful box inspiration to ferroelectric structures, either hydrogen bonded ferroelectrics, like these within the TGS kin, and oxide ferroelectrics, like natural and combined perovskites.

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**Additional info for Effective Field Approach to Phase Transitions And Some Applications to Ferroelectrics (World Scintific Lecture Notes in Physics)**

**Example text**

5) and (7) C = tanh "(*o/4fcn) (9) which is the desired equation of state giving the temperature dependence of the order parameter £. The transition temperature, at which (and above it) the order parameter becomes zero, is given, in terms of <&o = 2 $ A B — $AA-$BB, by (10) Tc = $O/4/=B. Equation (9) can be written in more explicit form as (tanh" 1 C)/C = Tc/T, (11) which allows one, expanding in a power series, as usual, the hyperbolic tangent, to get £(T) in the vicinity of the transition temperature as C(T) = v/3[(T c -T)/T] 1/2 (12) 42 Effective Field Approach to Phase Transitions The extra specific heat associated with the order-disorder process can be calculated in the following way.

1). , electron-phonon interaction, compared to the older, conventional superconductors? And, if this is not the case: which is the pairing mechanism in the new superconductors? In answering the first question, it seems to be clear that the upper theoretical limit in Tc for strong electronphonon coupled superconductors is about 40 K, well below the observed Tc = 125 K. Therefore, electron-phonon coupling alone does not seem sufficient to explain Cooper pairing in the new superconducting materials.

T h e evaluation of the integral in J e for complex atoms is not an easy task, and only approximate numerical results are available in most cases. However, these numerical results support values of 7 = 10 3 , of the right order of magnitude for exchange ferromagnets. 9 K ) , 5 actually exist, in which t h e effective field is of magnetic dipolar origin. In these systems values of 7 ss 1 can be expected. References 1. P. Weiss, J. Phys. 6, 667 (1907). 2. J. Dekker, Solid State Physics (Prentice Hall, Englewood Cliffs, NJ, 1962).

### Effective Field Approach to Phase Transitions And Some Applications to Ferroelectrics (World Scintific Lecture Notes in Physics) by Julio A. Gonzalo

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