1d Ising model without magnetic field has hamiltonian ##H=-J\sum^{N-1}_{i=1}S_iS_{i+1}## with no boundary condition has partition function ##Z_N=2^{N}\cosh^{N-1}(\beta J)##. In this model with magnetic field people often put into the game circular boundary condition because then they could solve problem using transfer matrix method. Is there any easy way to solve 1d Ising model without boundary condition in extern magnetic field. Hamiltonian of that model would be ##H=-J\sum^{N-1}_{i=1}S_iS_{i+1}-B\sum^{N}_{i=1}S_i##.(adsbygoogle = window.adsbygoogle || []).push({});

**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!

# With or without magnetic field.

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