Physics to Go! Part 2|教育線上App不用買

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!

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