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

Download Statistical Field Theory - Math Tripos - Past Exam Paper and more Exams Mathematics in PDF only on Docsity! MATHEMATICAL TRIPOS Part III Monday 2 June 2003 9 to 11 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 Explain briefly what is meant by a phase diagram. Give an example of a three– dimensional phase diagram which contains a tricritical point and describe the nature of the different transitions which may occur. Give an account of the Landau-Ginzburg theory of phase transitions in the context of a scalar field theory paying particular attention to the following topics: (a) The idea of an order parameter; (b) The occurrence of first-order and continuous phase transitions and how their defining properties are explained; (c) The Maxwell construction; (d) The features of a tricritical point. The critical indices in the λφ4 field theory are defined by M ∼ (−t)β , (h = 0) and M ∼ h1/δ , (t = 0) , where t = (T − TC)/TC , and h is the applied magnetic field. Calculate β and δ for both an ordinary and a tricritical point. Paper 46