13 research outputs found
Exact results for some Madelung type constants in the finite-size scaling theory
A general formula is obtained from which the madelung type constant: extensively used in the finite-size
scaling theory is computed analytically for some particular cases of the
parameters and . By adjusting these parameters one can obtain
different physical situations corresponding to different geometries and
magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added
On the Finite-Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations
The behavior of the finite-temperature C-function, defined by Neto and
Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d
-dimensional exactly solvable lattice model, recently proposed by Vojta [Phys.
Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as the
quantum nonlinear O(n) sigma model in the limit . The scaling
functions of C for the cases d=1 (absence of long-range order), d=2 (existence
of a quantum critical point), d=4 (existence of a line of finite temperature
critical points that ends up with a quantum critical point) are derived and
analyzed. The locations of regions where C is monotonically increasing (which
depend significantly on d) are exactly determined. The results are interpreted
within the finite-size scaling theory that has to be modified for d=4.
PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d,
02.30Comment: 15 pages LATEX, ioplppt.sty file used, 6 EPS figures. Some changes
made in section V (on finite-size scaling interpretation of the results
obtained
Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling
The quantum rotors model can be regarded as an effective model for the
low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we
consider a -dimensional model in the spherical approximation confined to a
general geometry of the form (
-linear space size and -temporal size) and subjected to periodic
boundary conditions. Due to the remarkable opportunity it offers for rigorous
study of finite-size effects at arbitrary dimensionality this model may play
the same role in quantum critical phenomena as the popular Berlin-Kac spherical
model in classical critical phenomena. Close to the zero-temperature quantum
critical point, the ideas of finite-size scaling are utilized to the fullest
extent for studying the critical behavior of the model. For different
dimensions and a detailed analysis, in terms of the
special functions of classical mathematics, for the susceptibility and the
equation of state is given. Particular attention is paid to the two-dimensional
case.Comment: 33pages, revtex+epsf, 3ps figures included submitted to PR