The final project counts for 25% of the course grade. Please choose one of the following two for a final project:

Research Project

Write a brief paper (two to four pages in Physical Review format) on a subject of your choice, relevant to the topics of this course. It should be formatted as a regular article with title, abstract, and bibliography. The main text should contain introductory and concluding paragraphs (whether or not they appear as subsections is not important).

The ideal project will involve a combination of literature review, discussion of an analytical or computational model, and application / analysis of experimental data.

Students can collaborate in groups provided that the respective contributions of the author of the joint paper is clearly specified in a footnote. (The length of the paper may be proportionately longer in such collaborations.) Clearly the initial hurdle is coming up with an interesting project that is doable in a short time.

Teaching Site

Design a web site that can be used to teach a topic related to Collective Behaviors to non-specialists. For example, imagine that a high school teacher of an honor-level science course would teach a one hour class session using the material on your web page. As such, you should include introductory materials, references that interested students can pursue on their own. The presentation must also be colorful and dynamic (e.g. by including figures, animations, applets, etc.) to engage and maintain the interests of a diverse non-specialist audience. As a model, you may wish to examine the following introduction to Bose–Einstein condensation.

This Year’s Projects

  • Percolation Model for Mobile Ad-hoc Random Networks
  • A BEG Model of Graphene Fluorination
  • Lee-Yang theorem
  • A Chern-Simons treatment of abelian topological defects in 2D
  • Explore phase transitions through percolation!
  • The error threshold in the quasispecies model as a phase transition in a 2-dimensional lattice model
  • Osmotic critical phenomena of semipermeable unilamellar vesicles
  • Position space renormalization of 2D Ising model with Dzyaloshinskii-Moriya Interaction
  • The Ising Model on a Binary Tree
  • A Closer Look at the Frustrated Ising Model on a Hierarchical Lattice and Possible Phase Diagram Modifications
  • Vortex-Magnetic Field Duality in the Classical XY Model
  • Theoretical Models for One and Two Component Lipid Membranes
  • Vanishing gaps in random transverse Ising model: Difficulty and new strategy for the Quantum Adiabatic Algorithm
  • Critical Exponents in Cytosolic Diffusion
  • The tensor-entanglement renormalization group of the 2D quantum rotor model
  • Studying the Six-Vertex Model with the Yang-Baxter Equation
  • Renormalization group on complex networks
  • Dislocation Mediated Melting in Triangular Lattice
  • Summary of several analytical studies of the BEG model
  • The Physics of Topological Defects
  • Memory-dependent Damping in Heisenberg Spin Chain
  • Renormalization of the Velocity Anisotropy due to Coulomb Interaction in 3D Semimetals
  • Density matrix renormalization group
  • Scaling behaviors of correlation measures in quantum spin systems
  • In search for phase transitions in Casimir force between percolating metal lattices

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