The cluster approximation and the method of correlation functions for multispin systems

A new approximate method for calculating the thermodynamic functions of multispin systems is considered for the example of the simplest Ising lattices. The idea of the method is based on the hypothesis that the Helmholtz energy of a system is obtained by averaging the Helmholtz energies of clusters over the lattice. The partition function of a cluster is found through usual spur calculations over the nodes constituting its nucleus followed by weighted averaging over the nearest-neighbor nodes. Some random correlated functions are used as weight functions. It is assumed that precisely these functions contain correlations between spins, that is, take into account some long-range order elements. Two clusters (mono- and binuclear) are considered, and two approaches are formulated. In the first approach, unknown parameters are determined using the variational principle. In the second one, temporal spin correlation functions are introduced, and the equations for parameter calculations are found from the boundary conditions for the temporal correlation functions. Both approaches are already equivalent to the Bete-Peierls approximation in the zeroth approximation

The cluster approximation and the method of correlation functions for multispin systems

A new approximate method for calculating the thermodynamic functions of multispin systems is considered for the example of the simplest Ising lattices. The idea of the method is based on the hypothesis that the Helmholtz energy of a system is obtained by averaging the Helmholtz energies of clusters over the lattice. The partition function of a cluster is found through usual spur calculations over the nodes constituting its nucleus followed by weighted averaging over the nearest-neighbor nodes. Some random correlated functions are used as weight functions. It is assumed that precisely these functions contain correlations between spins, that is, take into account some long-range order elements. Two clusters (mono- and binuclear) are considered, and two approaches are formulated. In the first approach, unknown parameters are determined using the variational principle. In the second one, temporal spin correlation functions are introduced, and the equations for parameter calculations are found from the boundary conditions for the temporal correlation functions. Both approaches are already equivalent to the Bete-Peierls approximation in the zeroth approximation

Vibrational modulation of spin-spin coupling and its effect on the spin dynamics of geminate radical pairs

[No abstract available

Vibrational modulation of spin-spin coupling and its effect on the spin dynamics of geminate radical pairs

[No abstract available

The Effect of Spin Coupling on the Spin Dynamics of Geminate Radical Pairs

[No abstract available

Spin-vibrational interactions in geminate radical pairs: Effective spin hamiltonian including anharmonicity

An equation for the effective spin Hamiltonian including the interaction of radical pair spins with vibrations in both linear and higher approximations was obtained. Even in the linear approximation, the Hamiltonian was found to be non-Heisenberg. The influence of a sound field on the probability of geminate radical pair recombination is considered in the Appendix. The results obtained can be of use for solving certain nanochemistry problems. © 2008 Pleiades Publishing, Ltd