Effect of sample size when using periodic boundary conditions in 2D Ising model

  • Thread starter DavidwN
  • Start date
  • #1
1
0
Hi,

I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model.

I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N?
I.e. if N is small I get a slow transition and as N is increased, the transition approaches a step function.

I don't understand why this is as I am only considering nearest neighbour interactions and by using periodic boundary conditions surely I am effectively modelling an infinite lattice? So why does the size of the unit cell affect my results?

Thanks!
 

Answers and Replies

  • #2
898
67
You are experiencing critical opalescence. As you approach the phase transition, the correlation length increases exponentially. When this domain size reaches the size of your simulation, then the simulation breaks down, i.e. does not describe the physics correctly anymore.

http://en.wikipedia.org/wiki/Ising_critical_exponents

Try and find a definition of the correlation length and calculated that on your grid. Then compare the temperature dependence for different grid sizes to what one would expect for an infinite lattice.
 

Related Threads on Effect of sample size when using periodic boundary conditions in 2D Ising model

Replies
1
Views
227
Replies
2
Views
3K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
16
Views
9K
Replies
1
Views
2K
Replies
2
Views
3K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
4
Views
3K
Top