Physics to Go! Part 2
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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
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
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
# 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
plot cycles: you can determine after
how many update cycles the new
spin configurations is plotted on the
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
By choosing "ordered" or "random"
you initialize the directions of the
spins either as all aligned or
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
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
In the lower panel the current
magnetization as well as the average
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
very nice simulation of statistical mechanics system
It is very well done and it runns quite fast. Suggestions for future improvements: allow saving the raw data of the magnetization, energy, etc; also it would be nice to be able to change the temperature while the program is running. Thank you!
- Category: Education
- Released: Mar 10, 2010
- Version: 1.0
- Size: 0.1 MB
- Language: English
- Seller: Stefan Schramm
- © Stefan Schramm
Compatibility: Requires iOS 3.0 or later. Compatible with iPhone, iPad, and iPod touch.