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1 - Introduction to phase transitions

from Part I - General Aspects

Published online by Cambridge University Press:  01 May 2025

Antoni Planes
Affiliation:
University of Barcelona
Avadh Saxena
Affiliation:
Los Alamos National Laboratory
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Summary

The chapter is an introduction to basic equilibrium aspects of phase transitions. It starts by reviewing thermodynamics and the thermodynamic description of phase transitions. Next, lattice models, such as the paradigmatic Ising model, are introduced as simple physical models that permit a mechano-statistical study of phase transitions from a more microscopic point of view. It is shown that the Ising model can quite faithfully describe many different systems after suitable interpretation of the lattice variables. Special emphasis is placed on the mean-field concept and the mean-field approximations. The deformable Ising model is then studied as an example that illustrates the interplay of different degrees of freedom. Subsequently, the Landau theory of phase transitions is introduced for continuous and first-order transitions, as well as critical and tricritical behaviour are analysed. Finally, scaling theories and the notion of universality within the framework of the renormalization group are briefly discussed.

Type
Chapter
Information
Phase Transitions
A Materials Perspective
, pp. 3 - 61
Publisher: Cambridge University Press
Print publication year: 2025

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