Parameter definitions for "neel"
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: In "neel", all of the energy parameters are taken to be dimensionless; only their relative values are of importance.
- temperature: the system temperature
- external field: an applied magnetic field with the convention that red spins are oriented parallel to the field if it is positive.
- exchange J: exchange interaction between nearest neighbors only, ferromagnetic if positive.
- dipole D: strength of the nearest neighbor dipole interaction, which falls off with distance to further neighbors as 1/r^n where n is chosen as 2 or 3 with the power law menu. See Appendix 14C of Simulations for Solid State Physics and below, for details of the angular dependence.
- sigma: rms magnitude of a random set of local fields which may be applied at the spin sites.
- number of sweeps: one sweep is 1800 Monte Carlo steps for the 30x60 array of spins in "neel". Once started, "neel" automatically shuts down after number of sweeps sweeps. To defeat this feature, set number of sweeps equal to a very large number, e.g., 1e4. (Restricted to positive integers.)
- MENUS
- easy axis: The spins in "neel" are Ising spins, i.e., they point only parallel or antiparallel to a specific direction, called the easy axis, taken here to be the direction of the applied field. That field (or the easy axis) may have one of several orientations with respect to the plane of the two-dimensional spin array, the plane of the monitor screen.
- perpendicular: the easy axis is perpendicular to the plane of the array. The dipolar interaction between any pair of spins is antiferromagnetic if the dipole D is positive.
- vertical: the easy axis lies in the plane of the array and is vertical on the screen. For positive D, the dipolar interaction is ferromagnetic for spins above and below one another, and antiferromagnetic for spins beside one another. It varies as cos(2*theta) where theta is the angle between the field and the vector connecting the two spins.
- horizontal: this case is similar to the vertical case, but rotated by 90 degrees..
- power law: determines the dependence of the magnitude of the dipolar interaction on distance between the spins.
- 2: gives an inverse square power law of energy of interaction which, together with an in-plane easy axis, allows simulation of a three dimensional ferromagnetic domain structure.
- 3: gives an inverse cube power law of the dipolar interaction energy.
- initial conditions: a selection from the menu establishes the corresponding initial conditions, or stores the existing configuration in memory.
- T=inf: spins randomly oriented.
- M=1: spins fully magnetized along the field.
- aferro: spins in perfect antiferromagnetic array.
- recall: recalls a stored configuration
- store: stores the existing configuration in memory for later recall. Spin orientations may be manually changed by clicking on individual spins or dragging slowly through the spin array with the cursor.
- TOGGLES
- run/stop: starts or stops the animation; key equivalent is the spacebar
- BUTTONS
- init: initializes the program as appropriate to the choice in the initial conditions menu, but does not reset the graph. Key equivalent is the i-key, and the program also initializes with the selection of an item from the initial conditions menu.
- reset: initializes the graph and the data arrays used for calculating time averages. This must be reset AFTER the initial conditions are set in order to have the first data point correct.
- copy graph: copies the graph for further manipulation and comparisons. See Graphs.
- 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 changes in the following system parameters:
- spin-up color: try a new color scheme for your tablecloth, or
- spin-down color: plaid scarf.
- speed: sets the number of sweeps per display, and gives an increase in speed near equilibrium at low temperatures where the spin array makes few changes, but has little effect at higher temperatures where the many spin flips make the calculation, not the display, the limiting factor on speed. (Restricted to positive integer.)
- 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 "neel"
Outputs
- DISPLAYS
- top: 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 slowly with the cursor.
- bottom: graph of normalized magnetization versus time with the unit of the time axis being one sweep.
- READOUTS All four of the following averages are taken over the time interval since the last reset. After the system parameters have been changed, these values are meaningless if additional data are taken without a reset.
- <M> : average magnetization.
- <(M-<M>)^2> : mean squared deviation of the magnetization from its mean.
- <E>: average value, per spin, of the system exchange and dipolar energies. The interaction energy with the external field is available from -MH.
- <(E-<E>)^2> : mean squared deviation of the energy from its mean.