174 research outputs found
Finite-size scaling in anisotropic systems
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_{\perp}) 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 corresponding spatial
directions, systems with space-"time"a anisotropy near a quantum critical point
and systems with Lifshitz points. The anisotropic properties involve also the
geometry of the systems. We consider systems confined to a d-dimensional layer
with geometry L^{m}\times\infty^{n}; m+n=d and periodic boundary conditions
across the finite m dimensions. The arising difficulties are avoided using a
technics of calculations based on the analytical properties of the generalized
Mittag-Leffler functions.Comment: 14 page
Mixed-state fidelity susceptibility through iterated commutator series expansion
We present a perturbative approach to the problem of computation of
mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical
techniques used provides an analytical expression for the MFS as a formal
expansion in terms of the thermodynamic mean values of successively higher
commutators of the Hamiltonian with the operator involved through the control
parameter. That expression is naturally divided into two parts: the usual
isothermal susceptibility and a constituent in the form of an infinite series
of thermodynamic mean values which encodes the noncommutativity in the problem.
If the symmetry properties of the Hamiltonian are given in terms of the
generators of some (finite dimensional) algebra, the obtained expansion may be
evaluated in a closed form. This issue is tested on several popular models, for
which it is shown that the calculations are much simpler if they are based on
the properties from the representation theory of the Heisenberg or SU(1, 1) Lie
algebra.Comment: 16 pages, Latex fil
Finite-Size Scaling and Long-Range Interactions
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
, where is the spatial dimension and the long-range
parameter . Classical and quantum systems are considered.Comment: 10 pages, Proceedings of the Bogolyubov Conference "Problems of
Theoretical and Mathematical Physics", Moscow-Dubna, September 2-6, 200
Comment on "Quantum critical paraelectrics and the Casimir effect in time"
At variance with the authors' statement [L. P\'{a}lov\'{a}, P. Chandra and P.
Coleman, Phys. Rev. B 79, 075101 (2009)], we show that the behavior of the
universal scaling amplitude of the gap function in the phonon dispersion
relation as a function of the dimensionality , obtained within a
self--consistent one--loop approach, is consistent with some previous
analytical results obtained in the framework of the --expansion in
conjunction with the field theoretic renormalization group method [S. Sachdev,
Phys. Rev. B 55, 142 (1997)] and the exact calculations corresponding to the
spherical limit i.e. infinite number of the components of the order
parameter [H. Chamati. and N. S. Tonchev, J. Phys. A: Math. Gen. 33, 873
(2000)]. Furthermore we determine numerically the behavior of the "temporal"
Casimir amplitude as a function of the dimensionality between the lower and
upper critical dimension and found a maximum at . This is confirmed
via an expansion near the upper dimension .Comment: 7 pages, 2 figure
Scaling behavior for finite O(n) systems with long-range interaction
A detailed investigation of the scaling properties of the fully finite systems with long-range interaction, decaying algebraically with the
interparticle distance like , below their upper critical
dimension is presented. The computation of the scaling functions is done to one
loop order in the non-zero modes. The results are obtained in an expansion of
powers of , where up to . The thermodynamic functions are found to be functions the
scaling variable , where and are the
coupling constants of the constructed effective theory, and is the linear
size of the system. Some simple universal results are obtained.Comment: 17 revtex pages, minor correction. new results and references are
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On the statistical mechanics of shape fluctuations of nearly spherical lipid vesicle
The mechanical properties of biological membranes play an important role in
the structure and the functioning of living organisms. One of the most widely
used methods for determination of the bending elasticity modulus of the model
lipid membranes (simplified models of the biomembranes with similar mechanical
properties) is analysis of the shape fluctuations of the nearly spherical lipid
vesicles. A theoretical basis of such an analysis is developed by Milner and
Safran. In the present studies we analyze their results using an approach based
on the Bogoljubov inequalities and the approximating Hamiltonian method. This
approach is in accordance with the principles of statistical mechanics and is
free of contradictions. Our considerations validate the results of Milner and
Safran if the stretching elasticity K_s of the membrane tends to zero.Comment: 8 pages, talk at the 18th International School on Condensed Matter
Physics, Sept. 2014, Varna, Bulgari
Some inequalities in the fidelity approach to phase transitions
We present some aspects of the fidelity approach to phase transitions based
on lower and upper bounds on the fidelity susceptibility that are expressed in
terms of thermodynamic quantities. Both commutative and non commutative cases
are considered. In the commutative case, in addition, a relation between the
fidelity and the nonequilibrium work done on the system in a process from an
equilibrium initial state to an equilibrium final state has been obtained by
using the Jarzynski equality.Comment: 4 page
Finite size and temperature effects in the model on a strip
Within Takahashi's spin-wave theory we study finite size and temperature
effects near the quantum critical point in the Heisenberg
antiferromagnet defined on a strip (). In the continuum limit,
the theory predicts universal finite size and temperature corrections and
describes the dimensional crossover in magnetic properties from 2+1 to 1+1
space-time dimensions.Comment: 4 PRB pages, no figure
Finite-size scaling properties and Casimir forces in an exactly solvable quantum statistical-mechanical model
A d-dimensional finite 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. Because of its close relation with the system of
quantum rotors it represents an effective model for studying the
low-temperature behaviour of quantum Heisenberg antiferromagnets. Close to the
zero-temperature quantum critical point the ideas of finite-size scaling are
used for studying the critical behaviour of the model. For a film geometry in
different space dimensions \half\sigma , where
controls the long-ranginess of the interactions, an analysis of
the free energy and the Casimir forces is given.Comment: Latex, 11 pages, elsart.cls, revised version with some minor
correction
Some new exact critical-point amplitudes
The scaling properties of the free energy and some of universal amplitudes of
a group of models belonging to the universality class of the quantum nonlinear
sigma model and the O(n) quantum model in the limit as
well as the quantum spherical model, with nearest-neighbor and long-range
interactions (decreasing at long distances as ) is
presented.Comment: 6 pages, 3 figures, Bogolubov conference: "Problems of theoretical
and mathematical physics", Moscow 1999, Russi
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