87 research outputs found
Finite-size scaling in systems with long-range interaction
The finite-size critical properties of the vector
model, with long-range interaction decaying algebraically with the
interparticle distance like , are investigated. The system
is confined to a finite geometry subject to periodic boundary condition.
Special attention is paid to the finite-size correction to the bulk
susceptibility above the critical temperature . We show that this
correction has a power-law nature in the case of pure long-range interaction
i.e. and it turns out to be exponential in case of short-range
interaction i.e. . The results are valid for arbitrary dimension ,
between the lower () critical
dimensions
Nematic order by thermal disorder in a three-dimensional lattice-spin model with dipolar-like interactions
At low temperatures, some lattice spin models with simple ferromagnetic or
antiferromagnetic interactions (for example nearest-neighbour interaction being
isotropic in spin space on a bipartite three-dimensional lattice) produce
orientationally ordered phases exhibiting nematic (second--rank) order, in
addition to the primary first-rank one; on the other hand, in the Literature,
they have been rather seldom investigated in this respect. Here we study the
thermodynamic properties of a three-dimensional model with dipolar-like
interaction. Its ground state is found to exhibit full orientational order with
respect to a suitably defined staggered magnetization (polarization), but no
nematic second-rank order. Extensive Monte Carlo simulations, in conjunction
with Finite-Size Scaling analysis have been used for characterizing its
critical behaviour; on the other hand, it has been found that nematic order
does indeed set in at low temperatures, via a mechanism of order by disorder.Comment: 24 pages, 9 figure
First order phase transitions in classical lattice gas spin models
The present paper considers some classical ferromagnetic lattice--gas models,
consisting of particles that carry --component spins () and
associated with a --dimensional lattice (); each site can host one
particle at most, thus implicitly allowing for hard--core repulsion; the pair
interaction, restricted to nearest neighbors, is ferromagnetic, and site
occupation is also controlled by the chemical potential . The models had
previously been investigated by Mean Field and Two--Site Cluster treatments
(when D=3), as well as Grand--Canonical Monte Carlo simulation in the case
, for both D=2 and D=3; the obtained results showed the same kind of
critical behaviour as the one known for their saturated lattice counterparts,
corresponding to one particle per site. Here we addressed by Grand--Canonical
Monte Carlo simulation the case where the chemical potential is negative and
sufficiently large in magnitude; the value was chosen for each of
the four previously investigated counterparts, together with in an
additional instance. We mostly found evidence of first order transitions, both
for D=2 and D=3, and quantitatively characterized their behaviour. Comparisons
are also made with recent experimental results.Comment: 9 pages, 12 figure
Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction
The finite size behavior of the susceptibility, Binder cumulant and some even
moments of the magnetization of a fully finite O(n) cubic system of size L are
analyzed and the corresponding scaling functions are derived within a
field-theoretic -expansion scheme under periodic boundary conditions.
We suppose a van der Waals type long-range interaction falling apart with the
distance r as , where , which does not change the
short-range critical exponents of the system. Despite that the system belongs
to the short-range universality class it is shown that above the bulk critical
temperature the finite-size corrections decay in a power-in-L, and not in
an exponential-in-L law, which is normally believed to be a characteristic
feature for such systems.Comment: 14 pages, revte
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
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