Statistical Field Theory - Mathematical Tripos - Old Exam, Exams of Mathematics

Download Statistical Field Theory - Mathematical Tripos - Old Exam and more Exams Mathematics in PDF only on Docsity! MATHEMATICAL TRIPOS Part III Friday 28 May, 2004 1.30 to 3.30 PAPER 46 STATISTICAL FIELD THEORY Attempt TWO 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 Maxwell construction, the occurrence of domains and the phenomenon of hysteresis; (d) The idea of critical exponents and how they may be derived; (e) The features of a tricritical point, how it occurs in LG theory and a brief description of a phase diagram containing a tricritical point. 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 46