Exactly Solvable Models (MAST90065)
Graduate courseworkPoints: 12.5Not available in 2020
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
About this subject
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
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In mathematical physics, a wealth of information comes from the exact, non-perturbative, solution of quantum models in one-dimension and classical models in two-dimensions. This subject is an introduction to this beautiful and deep subject. Yang-Baxter equations, Bethe ansatz and matrix product techniques are developed in the context of the critical two-dimensional Ising model, dimers, free fermions, the 6-vertex model, percolation, quantum spin chains and the stochastic asymmetric simple exclusion model. The algebraic setting incorporates the quantum groups, and the Temperley-Lieb and braid-monoid algebras.
Intended learning outcomes
After completing this subject students should:
- have learned how exactly solvable models apply to a variety of problems in applied mathematics and mathematical physics;
- appreciate the role of exact solutions and universality in mathematical physics and be able to use concepts of real and complex analysis to determine asymptotic behaviour;
- be able to compute correlation functions using matrix product techniques or random matrix theory;
- be familiar with the basic mathematical techniques of exactly solvable models including Yang-Baxter equation, Bethe Ansatz, commuting transfer matrices and matrix product states;
- understand the basic concepts of random matrix theory and appreciate their applicability;
- have the ability to pursue further studies in these and related areas.
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:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
The following subject, or equivalent:
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30021 | Complex Analysis |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
Corequisites
None
Non-allowed subjects
No disallowed subject combinations among new-generation subjects
Recommended background knowledge
It is recommended that students have completed the following subject, or equivalent:
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10007 | Linear Algebra |
Summer Term (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
No prior knowledge of physics is assumed.
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
| Description | Timing | Percentage |
|---|---|---|
Up to 40 pages of written assignments (two assignments worth 20% each, due mid and late in semester)
| Second half of the teaching period | 40% |
A written examination
| During the examination period | 60% |
Last updated: 3 November 2022
Dates & times
Not available in 2020
Time commitment details
3 contact hours and 7 hours private study per week.
Last updated: 3 November 2022
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022