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Notes, derivations, databases, applets, and other stuff

PhD thesis

• PhD thesis – "Studies of Strongly Correlated Electron Systems" – granular metals, magnetic droplets
• Carlson Group wiki (restricted access)

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All of the following are works in progress or abandoned projects.

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Bond propagation algorithm

• Bond propagation algorithm (for +/-J random-bond Ising model)
• Bond propagation algorithm for resistor networks: comparison with Gauss elimination

Monte Carlo simulations

These include a variety of algorithms (Metropolis, Glauber/Gibbs, Wolff, Heringa-Bloete geometric cluster).

• 2D XY model
• 2D Potts models
• 2D random-field Potts models
• Helicity modulus and Binder parameter of 2D Ising, 2D XY, 3D XY models
• Quantum Rotor model without dissipation: phase representation PIMC (path-integral Monte Carlo)
• Dissipative Quantum Rotor model: charge representation – doesn't work properly
• Ambegaokar-Eckern-Schoen model without dissipation: PIMC
• SU(N) "Heisenberg" antiferromagnets: SSE (Stochastic Series Expansion)

Other applets

• "Classical Lieb-Liniger model": Newton's cradle on a ring
• "Quantum Lieb-Liniger model": Visualizing the Bethe ansatz solution
• Iterative solution of Matsubara-frequency-dependent weak-coupling gap equation for superconductor
• Latticeland needs your help! (Holes and spins in the t-J model)
• Simulation of dimer model on square lattice using worm algorithm. The main point is that the ``clusters'' can be very large. (Doesn't seem to work in browser though...)

Notes

• Mapping from Ising model to dimer model (Fisher)
• Classical and quantum spin systems: perturbation theory about disordered and ordered states, mean-field theory, summary of known results, and so on
• Notes on Bethe ansatz (incomplete)
• Another set of notes on Bethe Ansatz (incomplete) -- including Lieb-Liniger model
• Diagrammatics for dirty metals: density response (polarisability) and current response (conductivity) - a bit stuck now

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Computing material

• Computing tips (mainly for Unix/Linux)
• More computing tips
• Algorithms
• tcsh script for compiling LaTeX, C++, and Java code
• Code for binary reblocking method for Monte Carlo error estimation: Fortran 90, C++, Java
• Code for Walker alias method for sampling from discrete probability distributions: Java
• Template for Java animation (free-running) – outdated
• Template for Java animation (free-running or click-driven) – outdated
• ComplexPlot.m : Mathematica package for plotting complex-valued functions with rainbow colo[u]rs, by Bernd Thaller   UNFORTUNATELY, doesn't work with Mathematica 6.

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Last updated Wednesday 05/27/09.