For a given hamiltonian H=-J∑SiSj -h∑SI in the one dimensional ising model, small h and capital J are applied magnetic field and strength of nearest neighbor interaction.Now how to evaluate derivative of with respect to the applied magnetic field evaluated at h=0.
The Hamiltonian H being contained in the expression for the density operator ρ, derivative with respect of h at h = 0 gives rise to (up to a constant multiplicative factor) Σm . Note that ≡ Tr[ρΑ].
Sir, actually I was able to calculate the four correlation ising spins (each spin can take values +1 or -1) in the absence of field. I was able to factorize it and get the following result which is just a product of two tan hyperbolic functions [tanh(K)]^(j-k) * [tanh(K)]^(m-l). Actually I was asked to take derivative of with respect to the applied field about the zero field from the above result which is calculated in the absence of the applied field. How do I do it sir ?
The Ising model in one dimension is an exactly-solved model. For details, consult the book Exactly Solved Models in Statistical Mechanics, by RJ Baxter (Dover, New York, 2007). The one-dimensional Ising model is the subject of Chapter 2 of this book.
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics