Use this form to generate a sequence of images from Monte Carlo evolution of an Ising Model system.

The actual calculations are done on a remote machine and can take some time depending on the specified parameters. The full Parameter Description List at the bottom of this document is good "reading material" while waiting for results.

The default parameter values in the form are all good starting points, and it is suggested that initial experimentation be limited to modest departures from these values.

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Descriptions Of Form Parameters

Basic Parameters

J/kT: The Initial Spin-Spin Coupling

"J" is the "strength" of the Spin-Spin interaction, and "kT" is the corresponding "strength" for random thermal fluctuations (as discussed in the Introductory Ising document). As long as the external magnetic field (the parameter "B", below), the ratio J/kT completely specifies the evolution of the Ising system.

Nsweeps: Number Of Grid Updates Per Image

A "Sweep" means an attempt to update (flip or not flip) all spin sites in the system. The parameter Nsweeps is simply the number of these full updates to be done for each generated picture.

Since each sweep makes only modest, localized changes in the spin configuration, we generally need a reasonably large number of sweeps (say, 50 or more) in order to have the Monte Carlo calculation stabilize at a reasonable result.

Number Of Pictures

This parameter is fairly obvious, giving the number of JPEG images (and associated correlation data) that will be generated. In order to complete the calculation in a reasonable amount of time, this number should be (well) less than ten.

J/kT Step: Coupling Change Between Pictures

This parameter specifies the amount by which the basic coupling changes between individual generated images. The value can be positive (temperature decreases), negative (temperature increases) or even zero (corresponding to several snapshots of system evolution at fixed temperature).

Additional/Advanced Parameters

Grid Layout: Specify The System Geometry

The integer value here selects a particular layout, as described in the indicated document. These layouts include not only different system sizes (numbers of spin states), but a few more exotic examples, such as boundary areas with fixed spin states and "holes" in the nominal grid of spins.

Be warned: Large grids take longer (the work done is proportional to the number of spin sites).

Initial State

This selects the system configuration before the start of the very first sweep, selecting from three different options:

• Initial Spin Values Are Random.
• All Spins Initially Point Up.
• All Spins Initially Point Down.

Sweep Pattern

Determines the order in which spin-flip attempts are made at the individual sites. The "Regular Sequence" option is an ordered march (left to right, top to bottom) across the system.

Update Stencil: Form Of The Spin-Spin Interaction

This parameter allows selection of a few "non-standard" alternatives to the simple, nearest-neighbor couplings used within the standard Ising model.

Warning: Selection of a non-standard update stencil will generally change the temperature at which the phase transition occurs.

State Resets

This can be used to force the calculation to restart from the specified initial configuration (all up, all down, or random) for each calculation and image in the requested set.

B/J: The External Magnetic Field

This option allows specification of an additional, external magnetic field in the full Ising Model energy formula (as discussed in the Introductory Ising document).

Warning: This term will completely "swamp" the dynamics of the system if it is very large, leading to really boring pictures.