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Ising model simulator on curved surfaces

  1. Jun 12, 2010 #1

    I am currently working on an open source project called Spinify. The Spinify
    project aims at producing an efficient simulation algorithm for the Ising
    model on surfaces with non trivial metric tensor. The project is still in its
    infancy, but I firmly believe that some very interesting results can come out
    of it.

    The project home page is at http://bitbucket.org/loicseguin/spinify/wiki/Home" [Broken].
    Volunteer developers and testers are needed in order
    to accelerate the development of the project. The software is written in C++
    and released under a BSD license. If you are interested in joining the project,
    send an email to the spinify-discuss@googlegroups.com mailing
    list and I will communicate with you.

    The current roadmap is a little vague, but among other things, lots of testing
    and code review is needed. Many more measures could be implemented and it
    would be interesting to study the feasibility of including some routines to try
    and calculate critical exponents for the model around the critical temperature.
    The only curved surface on which simulations can be run is the sphere.
    The next objective is to allow simulations on the torus and other surfaces of
    greater genus. I also work on a GUI. Up to now, I am writing the
    GUI in Objective-C and Cocoa, but I think it might be better to use some
    cross-platform toolkit such as Qt, Tk or wxWidget.

    Now, lets explain in a little bit more detail what Spinify is about. First of all,
    the Ising model is a very simple model of how magnetic
    materials become magnetized. A simple block of matter can be modelled as
    an arrangement of atoms, each of which has a spin. Spin is a quantum
    property of matter and, in the case of the Ising model, atoms can have
    a spin value of either +1 or -1. The reason for this is outside the scope
    of this wiki, but anyone interested in that can find more about it in any
    good introductory quantum mechanics book.

    If a material has magnetic properties (such as iron), the potential
    energy of two neighbouring atoms is lower if their spin is the same. Thus,
    since potential energy tends to be minimized, atoms try to get their spins
    all in the same direction. And since spin is associated with the magnetic
    field generated by the atom, all the magnetic fields add up together and
    form a macroscopic magnetic field.

    The Ising model makes many simplifying assumptions, the most important of
    which is that atoms only interact with their closest neighbours. This is
    reasonable since we know that the strength of a magnetic field decreases
    with the square of the distance. The Ising model has been studied in one
    and two dimensions extensively (the one dimensional Ising model is often
    an exercise in introductory statistical physics books; the two dimensional
    model on a square lattice has been solved by Onsager).

    The Spinify project aims at simulating the model on surfaces such as the
    sphere, the torus and the klein bottle. These surfaces have a non trivial
    metric tensor which is just a complicated way of saying that they are
    curved. This makes it hard, or sometimes even impossible, to embed a regular
    lattice on the surface. To circumvent this problem, we suggest to generate
    random lattices on the surface and then to run the simulation on that

    The project is motivated by conformal field theories which make
    interesting predictions on the behaviour of the Ising model on
    different surfaces in the limit where the number of atoms on the
    lattice tends to infinity. However, there are no proofs that the
    discrete model tends to the continuous model considered by CFT.

    The project started as an undergraduate research project at Université de
    Montréal in Canada a couple of years ago. But it has evolved a lot in the

    Thanks for you interest and have a great day,

    Loïc Séguin-C.
    Last edited by a moderator: May 4, 2017
  2. jcsd
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