Nicholay S. Tonchev

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The critical behavior of a quenched random hypercubic sample of linear size L is considered, within the "random-T(c)" field-theoretical model, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension d=4-epsilon and some universal results are obtained. The problem of(More)
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)
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)
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)
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)
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)
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)
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−σ , below their upper critical dimension is presented. The computation of the scaling functions is done to one loop order in the non-zero(More)
  • N S Tonchev
  • 2007
We present analytical results for the finite-size scaling in d-dimensional O(N) systems with strong anisotropy where the critical exponents (e.g., nu{ ||} and nu{ perpendicular}) depend on the direction. Prominent examples are systems with long-range interactions, decaying with the interparticle distance r as r{-d-sigma} with different exponents sigma in(More)