In this final chapter, three other aspects of the resistivity of metals and alloys will be discussed. As with many of the topics included in this book, each of these could easily justify a complete text in its own right and so the discussions here will be of necessity rather brief. It is hoped, however, that this introduction to these topics, all of which are still in a state of development, will serve to assist the interested reader in pursuing the matters in more detail.

Resistivity at the critical point

Some general comments

As noted in Chapter 2, a second order phase transition is characterised by a long range order parameter that continuously decays to zero as the critical transition temperature Tc is approached. Any of the physical properties of such a system which depend upon the derivative of S (or M) with respect to temperature, dS / dT (or dM//dT), such as the specific heat or temperature coefficient of resistivity dp/dT, will diverge at Tc. However, this gives a static picture of the transition which is somewhat misleading. Near Tc, small fluctuations in temperature produce fluctuations in the correlation parameter that are large in both magnitude and spatial extent. Since the resistivity is proportional to the magnitude of such correlations (the subject of Chapters 5 and 6), it is expected that the detailed behaviour at the critical point will be determined by these fluctuations.