Temporary HW

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Problem 1: Three Ising spins

Assume three spins 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 is give by:

(a) Find canonical partition function for this model.

(b) Find average spin .

(c) Find internal energy .

Problem 2: Spin-spin correlation function in the Ising model

Problem 3: Mean-field theory of the Heisenberg model of ferromagnetism