Nicholai S Tonchev

On the Finite-Size Scalling Equation for the Spherical Model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent σ, 0<σ⩽2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when σ<d<2σ. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.

On a class of exactly soluble statistical mechanical models with nonpolynomial interactions

The approximating Hamiltonian method of N. N. Bogolubov, Jr. is generalized to models with nonpolynomial intensive-observable interactions. The original Hamiltonian is proved to be thermodynamically equivalent to one linear in the intensive-observable trial Hamiltonian. We show that the exact expression for the free energy density in the thermodynamic limit can be obtained from a min-max principle for the system with trial Hamiltonian.