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 couplingthe 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 thereare 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 externalfield. Specify the amountof 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 thespins 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!
What's new in version 1.0
ReleaseAugust 25, 2010
Date AddedAugust 25, 2010
Additional RequirementsCompatible with iPhone, iPod Touch, and iPad. Requires iOS 3.1 or later. iTunes account required