Abstract:
The paper describes and analyzes a method for solving multiparticle quantum-mechanical problems based on the calculation of the density of states of the system as a function of the total energy and the projection of the magnetic moment. The method is applied to the calculation of the properties of a spin chain described by the Heisenberg Hamiltonian. The results are compared with the exact solution for a chain of $N$ = 16 spins obtained by the exact diagonalization method. It is shown that in the high-temperature region, the density of states method coincides with the exact solution. At temperatures less than the energy of the exchange interaction, the system is near the edge of the density of states and statistical methods do not work well. Thus, it is shown that the density of states method allows for efficient calculation of the characteristics even for a system with a small number of orderly arranged spins.
Keywords:density of states, spin chain, magnetic susceptibility, heat capacity, Heisenberg Hamiltonian.
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