🚀 go-pugleaf

In article <1992Dec22.051055.13451@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Brett McInnes) writes:
>marty@amaterasu.physics.uiuc.edu (Marty Gelfand) writes:
>:    Hey, who says conformal field theory is of no real use???  Down here
>: in low-energy physics it has been fruitful in problems such as
>                                   ^^^^^^^^^                              
> : quantum spin chains, multichannel Kondo systems,
>and 2D finite-temperature : critical phenomena (including random systems).
>: 
>Can you be a little more specific? I must admit that I am sceptical, but
>maybe I just attended some bad talks. However, I am willing to have my
>prejudices dispelled.

For 2D critical phenomena, conformal invariance provides a variety
of unexpected relationships among properties of critical points,
in particular, between critical exponents, finite-size scaling amplitudes,
and (this was harder) critical amplitude ratios, because they are all
related to the "central charge" c  of the critical model.  Conformal field
theory provides a classification scheme for 2D critical points
(due to Belavin, Polyakov, and Z.m.l.chikov):  if c is in a certain range, 
it must take on one of a sequence of discrete values, and if it does,
then all the critical exponents of the model are determined.
John Cardy has a review in vol 11 of Phase Transitions and Critical Phenomena
(Domb and Lebowitz, eds).

For applications to 1D quantum systems see, for example, I. Affleck et al,
J Phys A 22, 511 (1989) and references therein.   For other applications
take a look at anything done by Andreas Ludwig.

Sorry I can't give a brilliant exposition of this stuff, it's way 
beyond me.  --Marty Gelfand  marty@amaterasu.physics.uiuc.edu