Statistical Field Theory - Math Tripos - Past Exam, Exams of Mathematics

Download Statistical Field Theory - Math Tripos - Past Exam and more Exams Mathematics in PDF only on Docsity! MATHEMATICAL TRIPOS Part III Monday 3 June 2002 9 to 11 PAPER 64 STATISTICAL FIELD THEORY Attempt THREE questions There are three questions in total The questions carry equal weight You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator. 2 1 Give an account of the Landau-Ginsberg(LG) theory of phase transitions which should include a discussion of the following points: (a) The idea of an order parameter; (b) The distinction between first-order and continuous phase transitions and how their occurrence is predicted in LG theory; (c) The idea of critical exponents and how they may be derived; (d) The features of a tricritical point and how it occurs in LG theory; (e) The notion of critical dimension dc and why the predictions for critical exponents in LG theory fail for dimension d less than dc. For a system described by a single scalar field use LG theory to calculate two critical exponents of your choice at an ordinary critical point. Paper 64