Parameter definitions for "ising"

It's probably useful to look first at the special features page. You may also want to look at one of the general help files, Sliders, or Graphs.

Inputs

SLIDERS
- temperature: in units of J, where J is the nearest neighbor exchange energy (NOT joules). (A value temperature = 3 J implies a temperature T = 3J/k in kelvin with k being Boltzmann's constant.)
- external field: applied magnetic field, in units of J, where J is the nearest neighbor exchange constant. (A value external field = 3 J implies a field H = 3J/mu in tesla with mu being the magnetic moment of the spins.)
- number of sweeps: one sweep corresponds to a number of Monte Carlo steps equal to the total number of spins. "ising" shuts itself off after number of sweeps such sweeps. To defeat this feature, set this slider to a large number, e.g., 10^4. (Restricted to positive integers.)
- speed: sets the number of sweeps between successive displays, and hence the animation rate. Run long anneals at fast speeds, but watch individual spins adjust on the time scales of single sweeps. (Restricted to positive integers.)
MENUS
- initial conditions: the system can be initialized either by choosing an item from this menu, by clicking on the init button, or hitting the i-key:
  - T=inf: Click on T=inf (i.e., infinite temperature) to establish a random set of spin orientations.
  - M=1 Click on M=1 to establish a completely magnetized system.
  - recall Click on "recall" to bring up a spin configuration stored in memory.
  - store Any spin configuration may be stored in memory by choosing store from the menu when the desired spin configuration is in the display. Configurations may be tuned at will by clicking on individual spins to reverse them, or by dragging the cursor slowly across a series of spins.
- graph type The graph on the right can show three different characterizations of the time dependence of the magnetization:
  - magnetization: a direct plot of the normalized magnetization versus time. The unit of time is the characteristic time t0 for the relaxation of a spin to its own local field.
  - power spectrum: the squared Fourier transform of the deviation of the magnetization from its mean, evaluated over the total time available in the graph (NOT the smaller time interval that may have been selected by a zoom). The display shows a modified running average over average length successive points.
  - autocorrelation: The autocorrelation function of the deviation of the magnetization from its mean, taken over the full data set in the graph. It is also the Fourier transform of the power spectrum.
TOGGLES
- run/stop: starts and stops the animation; key equivalent is the spacebar.
BUTTONS
- init: sets the initial conditions for the next run as appropriate to the reading in the initial conditions menu, but does not reset the graph. Key equivalent is the i-key, and program also initializes with the selection of an item from the initial conditions menu.
- copy graph: copies the current graph for further manipulation or comparisons. See Graphs.
- reset: resets the graph to zero. This must be reset AFTER the initial conditions are set in order to have the first data point correct.
- presets: Takes you to a tear-off menu with which you may select the presets. For more details, see the preset item in the miscellaneous help file.
- configure: allows variation of additional system parameters.
  - lattice width: changes the number of spins in the array, as does the
  - lattice height: Again a compromise between better results with more spins, and faster results with fewer. (Both restricted to integers greater than one.)
  - spin-up color: for those who tire of red, and white, you may change
  - spin-down color: as well.
  - average length: power spectra are typically given as ensemble averages. "ising" achieves a similar result by calculating a running average over a series of average length successive points in the single sample power spectrum. (Restricted to positive odd integers)
  - revert: updates the listed configure parameters to the current values (which may have been changed by a preset command).
  - close: closes the configure window.
- help: Opens the help system which you have already found!
- quit: Terminates "ising"

Outputs

DISPLAYS

left side: illustrates the spin array, with red squares being up spins (parallel to a positive applied field) and white squares being down spins. Spins may be flipped manually with a click of the mouse or by dragging with the cursor.
right side: graphical output of one of the three characterizations chosen from the graph type menu above the graph. The unit of the time axis for the magnetization and the autocorrelation plots is t0, the characteristic time for the relaxation of a spin to its local field. The unit of frequency for the power spectrum is 1/t0. The magnetization is normalized to the saturation magnetization (hence maximum value of unity). The power spectrum is normalized such that its integral (over positive frequencies only) is one half of the mean square deviation of the magnetization. The autocorrelation function evaluated at tau=0 equals the mean square deviation of the magnetization.

READOUTS All four of these averages are taken over the time interval since the last reset. After the system parameters have been changed, values are meaningless if additional data are taken without a reset.

<M> : average magnetization.
<(M-<M>)^2> : mean squared deviation of the magnetization.
<E>: average value, per spin, of the system exchange energy. The interaction energy with the external field is not included, but is available from -<M>H.
<(E-<E>)^2> : mean squared deviation of the energy.