|
|
 | | From: | mike | | Subject: | Lattice types in 2d ising model | | Date: | Wed, 10 Nov 2004 05:11:52 -0600 |
|
|
 | Hi
Some time ago now I wrote a simple program in C++ to simulate the 2d
ising model on a square lattice which could calculate various
quantities such as specific heat capacity and so on. I started
thinking about this code again recently and thought that I might like
to extend it a little.
For example I was considering altering the lattice from the square one
that everyone seems to do to a triangular one. I am sure that this
has been done before and I was wondering if anyone out there knows if
I would see any different physics - such as will the transition
temperature change and so on.
Then I thought I might extend it to a 3d ising model on a cubic
lattice and possibly onto other lattices such as FCC, BCC and so on.
However I dont want to do this if I am not going to see anything
interesting in the results as its only really a hobby-type exercise
for me. Does anyone know of any references that may help me find out
what physics I may expect.
Finally - what sort of things do I need to think about including if
these simple Ising models are ever going to simulate REAL materials.
What is the difference between the basic 2D square lattice ising model
and ising models that correspond to real magnetic materials.
Thanks in advance for any replies
Mike
PS my email address is rather up and down at the moment so if you do
choose to reply could it be to the newsgroup please. Thanks again.
|
|
| | From: | Christophe | | Subject: | Re: Lattice types in 2d ising model | | Date: | Fri, 12 Nov 2004 06:40:03 -0600 |
|
|
| Hi,
> For example I was considering altering the lattice from the square one
> that everyone seems to do to a triangular one. I am sure that this
> has been done before and I was wondering if anyone out there knows if
> I would see any different physics - such as will the transition
> temperature change and so on.
It is well known that altering the lattice from square to any other
regular 2d lattice changes the critical temperature Tc. However, critical
exponents are not modified as predicted by Renormalisation Group. Random
lattices have also been studied.
> Then I thought I might extend it to a 3d ising model on a cubic
> lattice and possibly onto other lattices such as FCC, BCC and so on.
> However I dont want to do this if I am not going to see anything
> interesting in the results as its only really a hobby-type exercise
> for me. Does anyone know of any references that may help me find out
> what physics I may expect.
Idem. Different critical temperatures but same critical exponents.
> Finally - what sort of things do I need to think about including if
> these simple Ising models are ever going to simulate REAL materials.
> What is the difference between the basic 2D square lattice ising model
> and ising models that correspond to real magnetic materials.
The Hamiltonian is much more complex in real materials. In particular,
exhange couplings are not limited to nearest neighbour sites on the lattice
and the anisotropy is finite (it means that spins are really O(3)-vectors
(S_x,S_y,S_z) rather than up/down variables with an anisotropy energy
-K.S_z^2 or much more complex depending on the cristallographic structure).
Doing all this, you will again obtain different critical temperatures but
the same set of critical exponents.
Christophe
|
|
|
