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 $⟨s⟩$.

(c) Find internal energy $E$.