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Let's consider the one-dimensional Ising model with nearest neighbor interactions in the presence of a magnetic field. Show that the partition function $Z_N(T, B)$ is an even function of $B$ and compute its first non-vanishing term of the series expansion with respect to $B$.

   Let's consider the one-dimensional Ising model with nearest neighbor interactions in the presence of a magnetic field. Show that the partition function $Z_N(T, B)$ is an even function of $B$ and compute its first non-vanishing term of the series expansion with respect to $B$.
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Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
Giuseppe Mussardo 1st Edition
Chapter 2, Problem 4 ↓

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The Hamiltonian for the one-dimensional Ising model with nearest neighbor interactions in the presence of a magnetic field \( B \) is given by: \[ H = -J \sum_{i=1}^{N} s_i s_{i+1} - B \sum_{i=1}^{N} s_i \] where \( s_i = \pm 1 \) are the spin variables, \( J \)  Show more…

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Let's consider the one-dimensional Ising model with nearest neighbor interactions in the presence of a magnetic field. Show that the partition function $Z_N(T, B)$ is an even function of $B$ and compute its first non-vanishing term of the series expansion with respect to $B$.
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