Temporary HW

Problem 1: Three Ising spins

Assume three spins $s_{1},s_{2},s_{3}$ are arranged in an equilateral triangle with each spin interacting with its two neighbors. The energy expression for the Ising model in an external magnetic field $H$ is give by:

$H=-J(s_{1}s_{2}+s_{2}s_{3}+s_{3}s_{1})-F(s_{1}+s_{2}+s_{3})$

(a) Find canonical partition function for this model.

(b) Find average spin $\langle s\rangle$.

(c) Find internal energy $E$.