Introduction to Conformal Invariance and Its Applications to Critical Phenomena (Lecture Notes in Physics Monographs, 16) by Philippe Christe (PDF)

Description

The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau’s general theory of critical phenomena. In a dramatic development, Onsager’s exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a small piece of debate between my advisor and me. I’m a first year grad student in physics, wanting to do mathematical physics. She believes the book is “just great” but a bit “heavy” (meaning that a lot of information is written in a small space). On the other hand, I’ve found the text needlessly difficult to read.As an example of issues in the text, we can discuss their definition style.The authors will often italicize a new word. Great. We have some new terminology, yet none of it is actually defined in any sort of rigorous way. The definitions are assumed to be gleaned from context without laying any attempt to properly define anything. They also make use of terminology and assume that you’ve gotten the entire point without actually discussing it.Secondly, they don’t actually explain anything. My undergraduate background prepared me for each of the topics – I know about linear fractional maps – and I know about Lie algebras (from Humphreys’ also poor text on the subject), but these authors say “Having defined the conformal group and written down its Lie algebra,…” without actually mentioning that we have a Lie algebra corresponding to the conformal group. While the individual sentences that the authors are writing make sense, but they make little to no attempt to coherently describe what is happening, let alone to really discuss the physical ramifications.I thought chapter 2 would be better than chapter 1 as chapter 1 was a refresher on critical phenomena, but the second chapter is just as carelessly written. Hopefully the library will have other texts as an alternative to this. Definitely read from a local library before buying. Don’t hope for good exposition.Hopefully someone, somewhere will write a better text on the subject.

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