Question 705063

SCQHARD

Five classical spins are placed at the vertices of a regular pentagon. The Hamiltonian of the system is H=J∑SiSjH = J \sum S_i S_j where J>0,Si=±1J > 0, S_i = \pm 1 and the sum is over all possible nearest neighbour pairs. The degeneracy of the ground state is

(A)

8

(B)

5

(C)

4

(D)

10

Detailed Solution

By calculating the energy for all 25=322^5 = 32 possible configurations of the five spins S1,S2,S3,S4,S5S_1, S_2, S_3, S_4, S_5, we find that there are 10 states that yield the minimum energy E=−3JE = -3J.

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