Physics to Go!
Part 2 - spin systems 2 to 4 dimensions


The app calculates an interacting
system of spins (or magnets), including
the well-known Ising model as well as
more complex systems. You can
choose the system size for up to 4
dimensions. The updating of the spins
is done by a standard Monte-Carlo
heatbath algorithm.

Various options for the spin-spin
interaction are given. The coupling
strength as well as a constant external
field (acting in the vertical direction)
can be specified.



The controls on the main page are:   



  system size: set the number of
  in 2 to 4 directions (for a 2-dim
  system set nz and nt to 1). The total
  number of spins in the system is
  nx*ny*nz*nt.

  coupling: set the coupling strength
  between the spins (more accurately
  the coupling divided by the
  temperature). By changing the sign of
  the coupling the system tries to align
  spins in parallel (ferromagnetic) or
  anti-parallel (anti-ferromagnetic
  direction.


   # spins: you can set the number of
   possible spin directions. The choice
   of 2 corresponds to the Ising model
   (spin-up or spin-down). 4 means
   there are 4 possible directions (up,
   down, left, right) and so on.



   field: set the strength of a constant
   field pointing into the vertical
   direction. The spins try to align in this
   direction.



   plot cycles: you can determine after
   how many update cycles the new
   spin configurations is plotted on the
   screen.



   You can choose to periodically
   change the coupling strength or
   the external field. Specify the
   amount of change and the frequency
   of the update. With this option you
   can study phase transitions from
   disordered to ordered (spin-aligned)
   states. You can observe different
   transition behaviour depending on
   the number of dimensions or the type
 of interaction between the spins.
 


   There are several possibilites of
   interactions between spins. The
   "nearest neighbour" choice
   corresponds to the Ising model.
   You can also add the interaction of
   the spins with the diagonally adjacent
   neighbours. For the other two choices
   the spins interact will all other spins
   in the system. The interaction
   strength falls off either like 1 over
   distance (Coulomb potential) or
   exp(-distance) over distance (Yukawa
   potential).


   By choosing "ordered" or "random"
   you initialize the directions of the
   spins either as all aligned or
   randomly chosen.



 With "Turn" you reach the plot area.



   The averaged value of the spins
   (magnetization) and the standard
   deviation as well as the current value
   of the coupling and external field
   is shown.


   Below is the plotting frame showing
   the spins. The direction of the spins
   is shown by the direction of the
   symbols as well as the color.

   Below this area the spin, averaged
   over the system is displayed, where
   the direction is given by the spin
   orientation and the size of the symbol
   represents the absolute value of the
   magnetization.


   In the lower panel the current
   magnetization as well as the average
   value is
   shown.


   You start the updating of the spins
   by touching "Plot" (interrupt the
   calculation at any time by touching
   the panel again). Touching "Clear"
   clears the plotting area for the
   averaged magnetization.


                          Enjoy!