Physics – Condensed Matter
Scientific paper
1993-04-21
Springer Lecture Notes in Physics, Vol. m16 (1993)
Physics
Condensed Matter
xvi + 260 pages (here only the first xvi are given), Latex, UGVA-DPT 1992/11-794
Scientific paper
10.1063/1.2808642
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their application to the Ising, Potts, Ashkin-Teller and XY models, tricritical behaviour, the Yang-Lee singularity and the XXZ chain are presented. Finite-size scaling techniques and their conformal extensions are treated in detail. The vicinity of the critical point is studied using the exact $S$-matrix approach, the truncation method, the thermodynamic Bethe ansatz and asymptotic finite-size scaling functions. The integrability of the two-dimensional Ising model in a magnetic field is also dealt with. Finally, the extension of conformal invariance to surface critical phenomena is described and an outlook towards possible applications in critical dynamics is given.
Christe Philippe
Henkel Malte
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