Hey all,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 2 x 2 Ising lattice problem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**