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The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B 400, 525 (1993)], is analyzed within a d-dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B 53, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit n → ∞. The scaling… (More)

- Hassan Chamati, Ekaterina S. Pisanova, Nicholay S. Tonchev
- 1997

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 d–dimensional model in the spherical approximation confined to a general geometry of the form L d−d ′ ×∞ d ′ ×L z τ (L–linear space size and L τ –temporal size) and subjected to periodic boundary… (More)

- H Chamati, D M Danchev, N S Tonchev
- 2008

A d–dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and " temporal size " 1/T (T-temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions 1 2 σ < d < 3 2 σ , where 0 < σ ≤ 2 is a parameter controlling… (More)

- N. S. Tonchev
- 2004

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as 1/r d+σ , where d is the spatial dimension and the long-range parameter σ > 0. Classical and quantum systems are considered. A common wisdom is that the singularities in the thermodynamic functions at a critical… (More)

- H Chamati, N S Tonchev
- Physical review. E, Statistical, nonlinear, and…
- 2001

A detailed investigation of the scaling properties of the fully finite O(n) systems, under periodic boundary conditions, with long-range interaction, decaying algebraically with the interparticle distance r like r(-d-sigma), below their upper critical dimension, is presented. The computation of the scaling functions is done to one loop order in the nonzero… (More)

A general formula is obtained from which the Madelung type constant: C(d|ν) = ∞ 0 dxx d/2−ν−1 ∞ l=−∞ e −xl 2 d − 1 − π x d 2 extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters d and ν. By adjusting these parameters one can obtain different physical situations corresponding to… (More)

In this paper, we study in details the critical behavior of the O(n) quantum ϕ 4 model with long-range interaction decaying with the distances r by a power law as r −d−σ in the large n-limit. The zero-temperature critical behavior is discussed. Its alteration by the finite temperature and/or finite sizes in the space is studied. The scaling behaviours are… (More)

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