A linear ising chain of spins is not ferromagnetic because it can be easily broken. A single break of chain increases the energy by
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Answer:
Ferromagnetism arises when a collection of atomic spins align such that their associated magnetic moments all point in the same direction, yielding a net magnetic moment which is macroscopic in size. The simplest theoretical description of ferromagnetism is called the Ising model. This model was invented by Wilhelm Lenz in 1920: it is named after Ernst Ising, a student of Lenz who chose the model as the subject of his doctoral dissertation in 1925.
Consider $N$ atoms in the presence of a $z$-directed magnetic field of strength $H$. Suppose that all atoms are identical spin-$1/2$ systems. It follows that either $s_i=+1$ (spin up) or $s_i=-1$ (spin down), where $s_i$ is (twice) the $z$-component of the $i$th atomic spin. The total energy of the system is written:
\begin{displaymath}
E = - J\sum_{<i j>}s_i\,s_j -\mu\,H\sum_{i=1,N}s_i.
\end{displaymath} (351)
Here, $<i j>$ refers to a sum over nearest neighbour pairs of atoms. Furthermore, $J$ is called the exchange energy, whereas $\mu$ is the atomic magnetic moment. Equation (351) is the essence of the Ising model.
The physics of the Ising model is as follows. The first term on the right-hand side of Eq. (351) shows that the overall energy is lowered when neighbouring atomic spins are aligned. This effect is mostly due to the Pauli exclusion principle. Electrons cannot occupy the same quantum state, so two electrons on neighbouring atoms which have parallel spins (i.e., occupy the same orbital state) cannot come close together in space. No such restriction applies if the electrons have anti-parallel spins. Different spatial separations imply different electrostatic interaction energies, and the exchange energy, $J$, measures this difference. Note that since the exchange energy is electrostatic in origin, it can be quite large: i.e., $J\sim 1$eV. This is far larger than the energy associated with the direct magnetic interaction between neighbouring atomic spins, which is only about $10^{-4}$eV. However, the exchange effect is very short-range; hence, the restriction to nearest neighbour interaction is quite realistic.
Our first attempt to analyze the Ising model will employ a simplification known as the mean field approximation. The energy of the $i$th atom is written
\begin{displaymath}
e_i = -\frac{J}{2}\sum_{k=1,z}s_k\,s_i -\mu\,H\,s_i,
\end{displaymath}
Explanation: