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Exactly Solvable Models (MAST90065)
Graduate courseworkPoints: 12.5Not available in 2024
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: 31 January 2024
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30021 | Complex Analysis |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
Or equivalent
Corequisites
None
Non-allowed subjects
None
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: 31 January 2024
Assessment
| 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: 31 January 2024
Dates & times
Not available in 2024
Time commitment details
3 contact hours and 7 hours private study per week.
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Dover (2007).
- Related Handbook entries
This subject contributes to the following:
Type Name Course Doctor of Philosophy - Engineering Course Ph.D.- Engineering Course Master of Philosophy - Engineering Course Master of Science (Mathematics and Statistics) 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.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 31 January 2024