PY722 :: Statistical Physics II :: Fluctuations & Phase Transitions
Mo/We, 10:15 to 11:30, G100 Harrelson
Occasionally, classes will meet on Friday instead. Please keep this time clear.
Instructor: Karen Daniels, 258C Riddick, 919-513-7921, kdaniel@
Office hours: after class, Tuesday 3-4pm, or by appointment
Prerequisite: Familiarity with the laws of thermodynamics, kinetic theory of gases, 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.
Primary Text: James Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity. [Online Version]
Supplemental Texts: Readings from
Chandler, Introduction to Statistical Mechanics;
Chaikin & Lubensky, Principles of Condensed Matter Physics.;
Widom, Statistical Mechanics ;
Newman, Introduction to Networks;
and current scientific literature are posted at Hill Library Reserves
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?
Problem Sets: Detailed problem sets containing both analytical and computational problems are fundamental to learning the material in this class, will form the bulk of your grade, and will be assigned approximately biweekly. You will need to have access to a computer running Python for some of the computational exercises: see here for more information. For some problems, you may also find it helpful to use Matlab and/or Mathematica.
The problem sets will be due Fridays at noon on the date listed, unless otherwise specified. Email submissions are permitted, but please use a single PDF file. 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 exercises, you do not need to submit your .py 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. Solutions to the problem sets will be posted in a binder in the Grad Student Lounge. (added 3 Oct) The problem sets should take 8-10 hours per week to complete. The instructor welcomes information which aids in this calibration.
Blogging Assignments: Student will contribue to a shared blog which will serve as a journal club of current literature related to class topics. Blog assignments must be posted by Fridays at noon on the date listed. For each biweekly assignment, you will create a blog entry which:
- 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.
(added 3 Oct) 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 on Wednesdays following the due date to have a discussion about some of the issues raised by your postings.
Midterm exam: a take-home exam will be due on Friday, Oct 12 at noon.
Final paper: review-type paper and in-class presentation on a current application of a statistical physics topic. Examples from Fall 2009. Due Fri, Dec 7 at noon.
Grading: Your final grade will be calculated as follows: 50% problem sets, 10% blog entries, 20% take-home midterm exam, 20% final paper.
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.
(added 3 Oct) Sections 8.2 and 8.4 of the above policy are particularly applicable to our problem sets and bar the use of published solutions. There are honorable ways to obtain assistance, and to credit that assistance. Violations of this code will be treated seriously.
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.
This calendar is subject to change as the semester progresses. Some Friday make-up sessions will be scheduled at the usual class time, and are noted in red
- Random processes (Aug 20, 22)
Random walks, with and without correlations. Discrete vs. continuous models.
Reading: Sethna Chapters 1 and 2 (Note: Please review Chapter 3 on your own.)
- Intro to Python (Aug 27)
Reading: Getting Started pages (including the iPython tip sheet and the nano-tutorials as needed)
- Ergodicity and non-ergodicity (Aug 29)
Reading: Sethna Chapter 4
- Entropy, free energy, and ensembles (Sep 5, Sep 10, 12, 17)
Other ways to think about entropy: Shannon/information, pattern entropy. Entropic springs (e.g. rubbers, gels). Role of fluctuations in statistical physics. Depletion force.
Reading: Sethna Chapters 5, 6
- Ising model & computational techniques (Sep 17, 19, 21)
Reading: Sethna Chapter 8, Chandler Chapter 5 (on reserve)
- Order parameters & broken symmetries (Sep 26, Oct 1)
Reading: Sethna Chapter 9, Chandler Chapter 5 (on reserve)
- Correlation & response (Oct 3, 8, 10)
Spatial autocorrelation, susceptibilities, fluctuation-dissipation theorem
Reading: Sethna Chapter 10, Chaikin & Lubensky (on reserve)
- Research paper planning (Oct 15, 24)
Oct 24: librarian Ella Hu will provide a workshop on finding and using library resources
- Liquid and amorphous states (Oct 15, 17, 22)
Pair correlation function; scattering
Reading: Chandler Chapter 7 (on electronic reserves), Sethna Chapter 10, Widom Chapter 7 (on physical reserve)
- Phase transitions (Oct 29, 31)
Relationship between dynamical systems and phase transitions; interfacial energy; spinodal decomposition; nucleation; coarsening
Reading: Sethna Chapter 11, Chaikin & Lubensky (on reserve)
- Universality (Nov 5, 7)
Critical exponents; renormalization group; revisit percolation; rigidity percolation
Reading: Sethna Chapter 12, Chandler Chapter 5
- Statistical physics of networks (Nov 12, 16)
Random vs. small-world networks; phase transitions off the lattice
Reading: Newman, Chapters TBD
- Peer review of paper drafts (Nov 19)
- Student presentations (Nov 26, 28)
10-minute in-class talks on final papers
Problems in  might be useful for review, but are not assigned
- Blog1: commentary on a recent journal article which addresses randomness or lack of randomness (e.g. through correlations). Also, check that you can run the appropriate Python tools needed for next week's assignment. (due Fri, Aug 24)
- Computer Prep: We will use some class time on Monday to work with problem 2.13 (on HW next week), so please look over the materials carefully beforehand and try to starting running some of the code using these Python hints. You are welcome to bring your own laptop to class, or to use one of the Macs provided.
- HW1: Sethna Problems [1.2 optional], 1.3, 2.5, 2.10, 2.10c, 2.13
(due Fri, Aug 31)
- Ungraded, optional HW: review Sethna Problems 3.5, 3.8, 3.9 (solutions will be included with HW 1 solutions)
- Blog2: commentary on a recent journal article which addresses an issue of ergodicity, non-ergodicity, chaos, or entropy (due Sep 7, comments by Wed Sep 12)
- HW2: Sethna Problems 5.4, 5.9, 5.11, 6.11, and do something entropy-related with the posted solution to the Random Text as a starting point (5.14 or 5.15 might give you ideas; creativity will be rewarded; be prepared to share your results). (due Fri, Sep 14)
- Blog3: commentary on a recent journal article which contains an Ising-like model. Identify both the order parameter and any spontaneously-broken symmetries (due Fri Sep 21, comments by Wed Sep 26) Identify OP and SBS for 3 entries, and bring to class for discussion on Mon Oct 1
- HW 3: [Ising Model Exercises]
(due Fri Sep 28)
- Midterm: take-home exam (due Fri, Oct 12, noon)
- Blog 4: commentary on a recent journal article which addresses an issue related to correlations, susceptibility, fluctuation/dissipation, or radial distribution functions (due Fri, Oct 19; comment by Oct 22)
- HW 4: (due MON Oct 29, in class ) see emailed assignment
- Final paper topic proposal: due Wed, Oct 31, in class (see final_paper.pdf handout for details)
- Blog 5: commentary on a recent journal article on a phase transition (due Fri, Nov 2; comment by Wed Nov 7)
- Final paper draft outline: due Fri, Nov 9 at noon. (see final_paper.pdf handout for details)
- HW 5: (due Fri Nov 16, but no penalty if I have it by class time on Mon Nov 26). Chandler 5.6, and verify that p. 140 Eq. (a) satisfies the requirements of the Kadanoff tranformation (these are both analytic steps skipped in class). Sethna: Using either Java or Python play around with the ideas in 11.4, 11.6, 12.1 and write ~2-3 sentences about what you observed in each.
- Peer-edit: due Mon, Nov 26 in class. See peer_edit.pdf handout for details about your responsibilities.
- Presentations: Nov 26, 28 in class. See rubric.pdf handout for details of grading. Quantum Monday: Chen, Pan, Sang. Bio Wednesday: Countryman, Green, Strickland
- Final paper: due Fri, Dec 7 at noon. (the officially-scheduled Final Exam)