PY722 :: Statistical Physics II :: Fluctuations & Phase Transitions
Mo, 1:30 to 2:45, 314 Riddick Hall
We, 1:30 to 2:45, 143 Partners III (Starting Sept 3)
Instructor: Karen Daniels, 258C Riddick, 919-513-7921, kdaniel@...
Office hours: after class or by appointment
Prerequisite: Familiarity with the laws of thermodynamics, entropy, free energy, and ensembles, such as provided by PY721.
Course format: Upper-level graduate course with emphasis on current, inter-disciplinary applications and experiments, using both computational and analytic techniques.
Textbooks: The course will be topics-based rather than closely following a textbook. The main books we will reference are
These books, as well as other readings drawn from current scientific literature, will be available through Hill Library Reserves. Some are books, others are PDFs.
- Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity. [Online Version]
- Newman, Introduction to Networks
- Chandler, Introduction to Statistical Mechanics
- Chaikin & Lubensky, Principles of Condensed Matter Physics.
- Karder, Statistical Physics of Particles and Statistical Physics of Fields
Reading Assignments: You should read through the assigned chapters or papers prior to class, in enough detail to be able to answer questions of the following type: What were the key concepts introduced? What types of physical systems do the techniques in the reading apply to? What parts were difficult to understand? What mathematical techniques were used, and why? I expect students to take an active role in discussing material. A few times during the semester, you will make an informal 10-minute presentation to the class.
Assignments: For each topic you will solve one analytical problem and one computational problem related to the topic, and write one blog entry summarizing a current/classic application in your own field. These will approximately alternate weeks.
Computational problems can be completed in the language of your choice (Matlab, Python, Fortran, Mathematica, etc). Students may either use their own computer, or can make use of University resources.
Problem sets will be due in class a week or two following the end of each unit, unless otherwise specified (due dates will be provided for each assignment as they are created). Late assignments will lose 10% for each day late. Students are encouraged to work together, but each of you must present your own work and list who you worked with on each problem so as to give credit where it is due. Problem sets will be graded for both effort and accuracy. For computer-based exercises, you do not need to submit your raw code unless you have some reason you want me to look at it. Responses to text-based questions need to be in well-structured, complete sentences. For analytical problems, solutions will be posted in a binder in the Grad Student Lounge.
Blogging Assignments: Students will contribute to a shared blog which will serve as a journal club of current literature related to class topics. Blog assignments must be posted by the due date (usually set a week in advance, approximately alternating with problem sets). For each assignment, you will create a blog entry which:
You should spend approximately 60-90 minutes finding and reading your entry, and about 30-60 minutes looking over your classmates' submissions. Entries will be graded on a 0 to 2 scale where 0 = missing, 1 = minimally present or late, 2 = acceptable. Extra points may be awarded for outstandingly insightful entries. In addition, you will post at least one comment on a classmate's entry from the previous week (worth 1 additional point). We will take some time in the class immediately following each due date, to have a discussion about some of the issues raised by your postings.
- has an informative title
- is sorted into the appropriate category for that week's assignment
- contains a working link to a research paper which fits the description provided in that week's assignment
- contains an approximately 1-paragraph commentary on the paper. Topics you might address: Why is this paper important? How does the paper illustrate, complement, or contradict material covered in class? Why did the paper spark your interest? What interesting questions does the paper raise? Are any of the results or techniques surprising to you? The entry should not be a simple summary of the contents of the paper.
Workload: My goal is that homework assignments (including readings, blogs, problems) will require around 8 hours/week. You will have two weeks to work on each problem set (one per unit), and I welcome information which aids in calibrating this time estimate.
Final paper: The final exam will consist of a review-type paper and in-class presentation on a current application of a statistical physics topic. Examples from
Fall 2009 and
Grading: Your final grade will be calculated as follows: 60% problem sets, 10% blog entries, 30% final paper.
- Random Processes
Random walks, with and without correlations. Super- and sub-diffusion. Levy flights. Discrete vs. continuous models.
- Mon, 25 Aug: Read Sethna Chapter 2
- Wed, 27 Aug: non-Brownian diffusion and Levy flights. Read
[this] and [this] (both from Physics Today). Bring a copy of each to class (we will refer to them).
- Mon, 1 Sep: university closed for Labor Day, no class
- Blog entry #1: due Wed, 3 Sep. Come prepared to discuss why the paper you found exhibited sub- and/or super-diffusion.
- Wed Sept 3: Stokes-Einstein relation. If you're curious about Einstein's original papers:
- HW #1: due Wed, 10 Sep
Review of thermodynamic entropy. Entropic Spings. Free Energy. Depletion force. Other entropies: pattern, Shannon (information), Edwards (athermal).
- Mon, Sep 8: Read Sethna Sections 5.2 and 5.3.
- Wed/Mon, Sep 10/15: Entropic springs: read Sethna problem 5.12 and think about how you would approach the problem
- Wed, Sep 17: Depletion forces: [PDF]
- Mon, Sep 22: Other entropies, still from Sethna 5.2 and 5.3.
For additional context, you could look at these resources: Shannon's [original paper], [some context], Edwards' [original paper]
- Link to Shannon applet
- Blog entry #2: on entropy, posting due Wed, 17 Sep., comments due Mon 22 Sep
- HW #2: due Mon, 29 Sep [PDF]
- Interlude: Introduction to Percolation
- Sep 24: read Last and Thouless
- Oct 6: Guest Lecture: Thomas Halsey (ExxonMobil) -- Physics in the Oil Industry
- Ising Model and Order Parameters
Magnetic systems as a paradigm for phase transitions. Ising-like models of non-magnetic systems.
- Sep 29: Sethna Chapter 8, Chandler Chapter 5 (on reserve, will be particularly useful when we later talk about renormalization group)
- Oct 1: at least half of you should bring a laptop to class, read through HW#3 and complete sections 1 and 2 ahead of time on whatever machine you plan to use. Assistance will be available in class if it does't work.
- Oct 8: Translating between Ising-like models, observations of simulations, Markov models
- Online Java Ising Simulations,
or download the .jar archive and run it offline without browser objections
- Some Python help sites: python-guide.org and wiki python
- Blog entry #3: on an Ising model of something, posting due Mon Oct 6., comments due midnight Tuesday Oct 7
- HW #3: due Fri, Oct 17 (at 4pm) [PDF]
- Order Paramters, Correlation & Linear/Dynamic Response
Spatial autocorrelation function. Susceptibility. Fluctuation-Dissipation Theorem.
- Oct 13: order parameters (Sethna Ch 9, Chandler Ch 7);
- Oct 15: more order paratmers, intro to final paper
- Oct 20: librarian Karen Ciccone in ITTC Lab 2 in D.H. Hill, bring 3-4 paper topic ideas
- Oct 22: correlation functions (Sethna 10.3-10.4); susceptibility (10.5)
- Oct 27: fluctuation-dissipation theorem (10.6-10.9)
- Blog entry #4: on use of an order parameter, correlation function or a fluctuation-dissipation measurement. Posting due Mon Oct 27., comments due midnight Tues 28 Oct.
- HW #4: due Mon Nov 10 [PDF]
- Phase Transitions & Universality
Relationship between dynamical systems and phase transitions. Interfacial energy. Spinodal decomposition. Nucleation & Coarsening. Critical exponents. Renormalization group. Percolation.
Reading: Sethna Chapter 11 & 12, Chandler (Ch 5, on electronic reserve), Chaikin & Lubensky (on reserve)
- Nov 5: normal forms of phase transitions, nucleation -- via Skype in 415 Riddick
- Nov 10: coarsening
- Nov 12: mean field theory of Ising model, scaling exponents, criticality
- Nov 17: renormalization group
- Blog entry #5: on a phase transition being either first or second order. Posting due Mon Nov 17., comments due midnight Tues Nov 18.
- HW #5: Mon Nov 24 [PDF]
- Statistical Physics of Networks
Random vs. small-world networks. Phase transitions off the lattice.
- Final Papers
- Peer-editing of final paper drafts: Instructions
must be completed by Fri Dec 5
- Dec 1: 15-minute in-class talks (Scott, Yuming, Jon)
- Dec 3: 15-minute in-class talks (Sam, Drew), last chance to exchange drafts for peer-editing
- Due date: Wed, Dec 10 at 4pm (according to final exam calendar)
Honor Pledge: For all assignments, the instructor will assume that the student has upheld the NCSU Honor Pledge: "I have neither given nor received unauthorized aid on this test or assignment." Please refer to the Code of Student Conduct Policy for details.
Sections 8.2 and 8.4 of the above policy are particularly applicable to our problem sets and bar the use of published solutions.
Students with disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation REG 02.20.01.