- #1
shetland
- 17
- 0
Hey all,
I have a problem I'm working on. A 2 x 2 ising lattice,
[tex]
\ H = K_1\sum_{nn}\sigma_i\sigma_j \ + \ K_2\sum_{nnn}\sigma_i\sigma_j \ + \ K_3\sum_{sg}\sigma_i\sigma_j\sigma_k\sigma_l
[/tex]
Were to find H as an explicit function the sigma's,
[tex] H(\sigma_1,\sigma_2,\sigma_3,\sigma_4)[/tex]
Its the typical spin lattice situation, with [tex]\sigma = =\pm1[/tex]
For those in the know, one standard way is to use renormalization. But wouldn't this arrive at a function of H only in terms of the new K? Another way would be to set up a transfer matrix method...but I haven't been exposed to this before.
Also, if I understand the process of re-normalization, I guess in a finite example like the 2x2, is the goal to reduce the degrees of freedom to one, meaning some ultimate K for site 1?
Any help/suggestions would be greatly appreciated.
Shelley
I have a problem I'm working on. A 2 x 2 ising lattice,
[tex]
\ H = K_1\sum_{nn}\sigma_i\sigma_j \ + \ K_2\sum_{nnn}\sigma_i\sigma_j \ + \ K_3\sum_{sg}\sigma_i\sigma_j\sigma_k\sigma_l
[/tex]
Were to find H as an explicit function the sigma's,
[tex] H(\sigma_1,\sigma_2,\sigma_3,\sigma_4)[/tex]
Its the typical spin lattice situation, with [tex]\sigma = =\pm1[/tex]
For those in the know, one standard way is to use renormalization. But wouldn't this arrive at a function of H only in terms of the new K? Another way would be to set up a transfer matrix method...but I haven't been exposed to this before.
Also, if I understand the process of re-normalization, I guess in a finite example like the 2x2, is the goal to reduce the degrees of freedom to one, meaning some ultimate K for site 1?
Any help/suggestions would be greatly appreciated.
Shelley