389 research outputs found
Spin Frustration and Orbital Order in Vanadium Spinels
We present the results of our theoretical study on the effects of geometrical
frustration and the interplay between spin and orbital degrees of freedom in
vanadium spinel oxides VO ( = Zn, Mg or Cd). Introducing an
effective spin-orbital-lattice coupled model in the strong correlation limit
and performing Monte Carlo simulation for the model, we propose a reduced spin
Hamiltonian in the orbital ordered phase to capture the stabilization mechanism
of the antiferromagnetic order. Orbital order drastically reduces spin
frustration by introducing spatial anisotropy in the spin exchange
interactions, and the reduced spin model can be regarded as weakly-coupled
one-dimensional antiferromagnetic chains. The critical exponent estimated by
finite-size scaling analysis shows that the magnetic transition belongs to the
three-dimensional Heisenberg universality class. Frustration remaining in the
mean-field level is reduced by thermal fluctuations to stabilize a collinear
ordering.Comment: 4 pages, 4 figures, proceedings submitted to SPQS200
Critical Exponents of the pure and random-field Ising models
We show that current estimates of the critical exponents of the
three-dimensional random-field Ising model are in agreement with the exponents
of the pure Ising system in dimension 3 - theta where theta is the exponent
that governs the hyperscaling violation in the random case.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.
Scaling Analysis of Chiral Phase Transition for Two Flavors of Kogut-Susskind Quarks
Report is made of a systematic scaling study of the finite-temperature chiral
phase transition of two-flavor QCD with the Kogut-Susskind quark action based
on simulations on (=8, 12 and 16) lattices at the quark mass of
and 0.01. Our finite-size data show that a phase
transition is absent for , and quite likely also at .
The scaling behavior of susceptibilities as a function of is consistent
with a second-order transition at . However, the exponents deviate from
the O(2) or O(4) values theoretically expected.Comment: Talk presented by M. Okawa at the International Workshop on ``
LATTICE QCD ON PARALLEL COMPUTERS", 10-15 March 1997, Center for
Computational Physics, University of Tsukuba. 7 LaTeX pages plus 5 postscript
figures, uses espcrc2.st
Critical adsorption at chemically structured substrates
We consider binary liquid mixtures near their critical consolute points and
exposed to geometrically flat but chemically structured substrates. The
chemical contrast between the various substrate structures amounts to opposite
local preferences for the two species of the binary liquid mixtures. Order
parameters profiles are calculated for a chemical step, for a single chemical
stripe, and for a periodic stripe pattern. The order parameter distributions
exhibit frustration across the chemical steps which heals upon approaching the
bulk. The corresponding spatial variation of the order parameter and its
dependence on temperature are governed by universal scaling functions which we
calculate within mean field theory. These scaling functions also determine the
universal behavior of the excess adsorption relative to suitably chosen
reference systems
Critical exponents for 3D O(n)-symmetric model with n > 3
Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated
on the base of six-loop renormalization-group (RG) expansions. A simple
Pade-Borel technique is used for the resummation of the RG series and the Pade
approximants [L/1] are shown to give rather good numerical results for all
calculated quantities. For large n, the fixed point location g_c and the
critical exponents are also determined directly from six-loop expansions
without addressing the resummation procedure. An analysis of the numbers
obtained shows that resummation becomes unnecessary when n exceeds 28 provided
an accuracy of about 0.01 is adopted as satisfactory for g_c and critical
exponents. Further, results of the calculations performed are used to estimate
the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to
play the role of the lower boundary of the domain where this approximation
provides high-precision estimates for the critical exponents.Comment: 10 pages, TeX, no figure
Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory
By large scale Monte Carlo simulations it is shown that the stable fixed
point of the SO(5) theory is either bicritical or tetracritical depending on
the effective interaction between the antiferromagnetism and superconductivity
orders. There are no fluctuation-induced first-order transitions suggested by
epsilon expansions. Bicritical and tetracritical scaling functions are derived
for the first time and critical exponents are evaluated with high accuracy.
Suggestions on experiments are given.Comment: 11 pages, 8 postscript figures, Revtex, revised versio
Critical behavior of the 3-state Potts model on Sierpinski carpet
We study the critical behavior of the 3-state Potts model, where the spins
are located at the centers of the occupied squares of the deterministic
Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo
simulations, for a Hausdorff dimension . The phase
transition is shown to be a second order one. The maxima of the susceptibility
of the order parameter follow a power law in a very reliable way, which enables
us to calculate the ratio of the exponents . We find that the
scaling corrections affect the behavior of most of the thermodynamical
quantities. However, the sequence of intersection points extracted from the
Binder's cumulant provides bounds for the critical temperature. We are able to
give the bounds for the exponent as well as for the ratio of the
exponents , which are compatible with the results calculated from
the hyperscaling relation.Comment: 13 pages, 4 figure
Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study
We perform a Monte Carlo Renormalization Group analysis of the critical
behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with
Hausdorff dimension . This method is shown to be relevant to
the calculation of the critical temperature and the magnetic
eigen-exponent on such structures. On the other hand, scaling corrections
hinder the calculation of the temperature eigen-exponent . At last, the
results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure
Algebraic Self-Similar Renormalization in Theory of Critical Phenomena
We consider the method of self-similar renormalization for calculating
critical temperatures and critical indices. A new optimized variant of the
method for an effective summation of asymptotic series is suggested and
illustrated by several different examples. The advantage of the method is in
combining simplicity with high accuracy.Comment: 1 file, 44 pages, RevTe
Power-law correlations and orientational glass in random-field Heisenberg models
Monte Carlo simulations have been used to study a discretized Heisenberg
ferromagnet (FM) in a random field on simple cubic lattices. The spin variable
on each site is chosen from the twelve [110] directions. The random field has
infinite strength and a random direction on a fraction x of the sites of the
lattice, and is zero on the remaining sites. For x = 0 there are two phase
transitions. At low temperatures there is a [110] FM phase, and at intermediate
temperature there is a [111] FM phase. For x > 0 there is an intermediate phase
between the paramagnet and the ferromagnet, which is characterized by a
|k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM
phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has
disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure
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