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Ground state degeneracy: Spin vs Fermionic language
Let us first consider the Hamiltonian of well-known 1D periodic Ising model as
$$
H = -\frac{1}{2} \sum_{j=1}^N \sigma^x_j \sigma^x_{j+1} + \frac{h}{2}\sum_{j=1}^N \sigma^z_j.
$$
Now, in the ...
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17
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Phase Transition in the Ising Model with Non-Uniform Magnetic Field
Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by
$$
H^{\omega}_{\Lambda}(\sigma)=-J\sum_{...
Leandro