Introduction to Conformal Invariance and its Applications to Critical Phenomena

Philippe Christe; Malte Henkel

doi:10.1063/1.2808642

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arXiv · cond-mat/9304035

Introduction to Conformal Invariance and its Applications to Critical Phenomena

Philippe Christe·Malte Henkel

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Abstract

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.

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Philippe Christe, Malte Henkel. 1993-04-21. Introduction to Conformal Invariance and its Applications to Critical Phenomena. https://doi.org/10.1063/1.2808642

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