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IsingLite

Some fun with Ising Model and Monte Carlo methods

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IsingLite

Some fun with 2-dimensional Ising model and algorithms as Heat Bath, Metropolis and Wolff. This package provides functions to create and play with simples simulations and Monte Carlo algorithms.

Installation

To install this package, inside Julia REPL, type:

Pkg.clone("git://github.com/brk00/IsingLite.jl.git")

Usage

This package is intended to be used from inside the Julia REPL. To load the package, after installing it, type:

using IsingLite

Creating a spin grid

A n by n random grid of spins can be created by using the spingrid function. The grid created is a simple 2-dimensional Julia Array, and not a special data type. Example:

g = spingrid(10) # Create a 10x10 spin grid

Running algorithms on spin grids

This package supports heatbath, matropolis and wolff algorithms for the Ising Model. To run any of these, you can use the respective function on a previously created spin grid. Example:

g = spingrid(25) #Create a spin grid

heatbath!(g)

The function will return an array with the values of magnetization of the grid after each iteration. Also, a plot showing the magnetization of the grid by the number of iterations will be saved on working directory.

You can add keyword arguments to the algorithms' functions:

heatbath!(g, verbose=false)

All functions (heatbath!, metropolis!, wolff!) support basically the same API. The supported keyword arguments are:

  • h, a Float64 number indicating the value of the external field (default is 0.0)
  • temp, a Float64 number indicating the temperature of the simulation (default is 1.0)
  • iters, an Integer indicating the number of iterations to be performed (default is 5000 in the case of heatbath! and metropolis!, and 30 in the case of wolff!)
  • plot, a Bool indicating if the user want or not to plot the result (default is true)
  • verbose, a Bool indicating if the user want the function to print something during or after the run (default is true)

Producing Phase Diagrams

You can produce a phase diagram, by calling the diagram function, which returns two arrays: one of temperatures and the other of the grid's magnetization at each temperature. Example:

t, m = diagram(heatbath!)

The only non-optional argument of the diagram function is a function f implementing the algorithm you want. As said before, this package only provide the functions heatbath!, metropolis!, and wolff!, but you can pass any function with the same API of these (detailed on the previous section), and the diagram will produce a phase diagram accordingly. This function also support many keyword arguments:

  • size, a Integer with the size of the spin grid used to generate the diagram (default is 10)
  • ensembles, an Integer denoting the number of ensembles (default is 50)
  • h, a Float64 number indicating the value of the external field (default is 0.0)
  • mintemp, a Float64 number indicating the temperature at which the simulation starts (default is 0.5)
  • step, a Float64 number indicating by what value the temperature changes at each iteration (default is 0.2)
  • maxtemp, a Float64 number indicating the temperature at which the simulation end (default is 0.5)
  • iters, an Integer indicating the number of iterations to be performed inside the given algorithm (default is 5000)
  • plot, a Bool indicating if the user want or not to plot the result (default is true)
  • verbose, a Bool indicating if the user want the function to print something during or after the run (default is true)

Auxiliary functions

The function neighbors receives a grid g, and two coordinates i and j inside it, and return an Array of coordinates (each one in a tuple of the kind (x,y)) of it's neighbors. Example:

g = spingrid(10)

# Get the coordinates of the neighbors of g[1,1]
neighbors(g, 1, 1) # Returns [(2,1), (1,2)]

The function nspins receives a grid g, and two coordinates i and j inside it, and return an Array of spins surrounding it.

g = spingrid(10)

# Get the spins of the neighbors of g[1,1]
nspins(g, 1, 1)

First Commit

07/15/2014

Last Touched

about 1 month ago

Commits

2 commits

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