Exactly Solvable Models
Subject MAST90065 (2013)
Note: This is an archived Handbook entry from 2013.
Credit Points:  12.50 

Level:  9 (Graduate/Postgraduate) 
Dates & Locations:  This subject is not offered in 2013. 
Time Commitment:  Contact Hours: 36 hours comprising two 1hour lectures and one 1hour practice class per week Total Time Commitment: 3 contact hours and 7 hours private study per week. 
Prerequisites:  The following subject, or equivalent: Subject Study Period Commencement: Credit Points: 
Corequisites:  None 
Recommended Background Knowledge:  It is recommended that students have completed the following subject, or equivalent: Subject Study Period Commencement: Credit Points: No prior knowledge of physics is assumed. 
Non Allowed Subjects:  No disallowed subject combinations among newgeneration subjects 
Core Participation Requirements: 
For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry. The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/ 
Contact
Assoc Prof Jan de Gier
Email: jdgier@unimelb.edu.au
Prof Peter Forrester
Email: pjforr@unimelb.edu.au
Subject Overview: 
In mathematical physics, a wealth of information comes from the exact, nonperturbative, solution of quantum models in onedimension and classical models in twodimensions. This subject is an introduction into YangBaxter and Bethe Ansatz integrability, and the orthogonal polynomial method of random matrix theory. Transfer matrices, YangBaxter equation and Bethe ansatz are developed in the context of the 6vertex model, quantum spin chains and other examples. As a solvable model, random matrix theory aims to first identify the explicit eigenvalue distributions for a given matrix distribution. The method of orthogonal polynomials is then used to compute eigenvalue correlation functions that can be compared against (numerical) experiments. 

Objectives: 
After completing this subject students should:

Assessment: 
Up to 40 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3hour written examination (60%, in the examination period). 
Prescribed Texts:  None 
Recommended Texts:  R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Dover (2007). 
Breadth Options:  This subject is not available as a breadth subject. 
Fees Information:  Subject EFTSL, Level, Discipline & Census Date 
Generic Skills: 
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

Related Course(s): 
Master of Philosophy  Engineering Master of Science (Mathematics and Statistics) Ph.D. Engineering 
Related Majors/Minors/Specialisations: 
Mathematics and Statistics 
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