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### app_style ising command

### app_style ising/single command

**Syntax:**

app_style style

- style =
*ising* or *ising/single*

**Examples:**

app_style ising
app_style ising/single

**Description:**

These are on-lattice applications which evolve a 2-state Ising model,
where each lattice site has a spin of 1 or 2. Sites flip their spin
as the model evolves.

The Hamiltonian representing the energy of site I is as follows:

Hi = Sum_j delta_ij

where Sum_j is a sum over all the neighbor sites of site I and
delta_ij is 0 if the spin of sites I and J are the same and 1 if they
are different. The energy of the entire system is the sum of Hi over
all sites.

This application performs Glauber dynamics, meaning the spin is
flipped on a single site. See app_style
diffusion for an Ising model which performs
Kawasaki dynamics, meaning the spins on two neighboring sites are
swapped.

As explained on this page, this application can be
evolved by either a kinetic Monte Carlo (KMC) or rejection KMC (rKMC)
algorithm. You must thus define a KMC solver or sweeping method to be
used with the application via the solve_style or
sweep commands.

For solution by a KMC algorithm, a site event is a spin flip and its
probability is min[1,exp(-dE/kT)], where dE = Efinal - Einitial
using the Hamiltonian defined above for the energy of the site, and T
is the temperature of the system defined by the
temperature command (which includes the Boltzmann
constant k implicitly).

For solution by a rKMC algorithm, the *ising* and *ising/single*
styles use a different rejection-based algorithm. For the *ising*
style, the spin is set randomly to 1 or 2. For the *ising/single*
style, the spin is flipped to its opposite value. In either case, dE
= Efinal - Einitial is calculated, as is a uniform random number R
between 0 and 1. The new state is accepted if R <
min[1,exp(-dE/kT)].

The following additional commands are defined by this application:

**Restrictions:** none

**Related commands:**

app_style potts

**Default:** none