A quantum system is described by the Hamiltonian
H = JSz + λSx
where \(S_i=\frac{\hbar}{2} \sigma_i \) and σi (i = x, y, z) are the Pauli matrices. If 0 < λ << J, then the leading correction in λ to the partition function of the system at temperature T is
1
\(\frac{h \lambda^2}{2 J k_B T} \operatorname{coth}\left(\frac{J h}{2 k_B T}\right) \)
2
\(\frac{h \lambda^2}{2 J k_B T} \tanh \left(\frac{J h}{2 k_B T}\right) \)
3
\(\frac{h \lambda^2}{2 J k_B T} \cosh \left(\frac{J h}{2 k_B T}\right) \)
4
\(\frac{h \lambda^2}{2 J k_B T} \sinh \left(\frac{J h}{2 k_B T}\right) \)