ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 82B10, 82B20, 82B23 Danchev, Daniel Marinov, Institute of Mechanics, Bulgarian Academy of Sciences Fss Properties of an Exactly Solvable Quantum Model The scaling function of the free energy and the finite temperature Cfunction, as well as the “temporal” Casimir amplitudes Δ(d) of the recently proposed quantum spherical model under periodic boundary conditions and geometry ∞^{d−1} × T^{−1} are analytically derived and analyzed. We consider the case of a short-range interaction and some special cases of longrange interactions decreasing at long distances as 1/r^{d+σ} with 0 < σ ≤ 2. Special attention is paid on the d = σ case where the result Δ(σ) = −16ζ(3)/ [5σ (4π)^{σ/2} Γ (σ/2)] is obtained. It is shown that the monotonicity of the C-function, as a function of the temperature, depends on the existence of a phase transition in the finite- and/or zero-temperature system. References [1] D. Danchev, Phys. Rev. E, 53 (1996) 2104–2109.

[2] H. Chamati, D. M. Danchev and N. S. Tonchev, cond-mat/9709115, to appear in J. Theor. Appl. Mech., Sofia.