- #1

mahblah

- 21

- 2

## Homework Statement

Find the ground state (stable configuration at T = 0) of the one-dimensional ising model with first and second neighbour intercations:

[itex] H = -J_1 \sum_{i} s_i s_{i+1} -J_2 \sum_{i} s_i s_{i+2} [/itex]

where [itex] s_i = \pm 1 [/itex]

## The Attempt at a Solution

I really don't know what i should do.. i don't know what i must FIND, this is my problem!

maybe i must find the Partition function and calculate the average magnetization ? so i say:

[itex] Z = \sum_{s} \exp{[-\beta H]} = (2 \cosh(\beta J_1) \cosh(\beta J_2))^N [/itex]

but seems that:

[itex] <s>_{T=0} = \frac{ \sum_{s} \exp{[-\beta H]} \sum_{i}s_i } {\sum_{s} \exp{[-\beta H]}} =0 [/itex]

i'm not interested about solution, but i want to know what i must do---

thanks all,

mahblah.

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