419 research outputs found
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
In view of the recently seen dramatic effect of quenched random bonds on
tricritical systems, we have conducted a renormalization-group study on the
effect of quenched random fields on the tricritical phase diagram of the spin-1
Ising model in . We find that random fields convert first-order phase
transitions into second-order, in fact more effectively than random bonds. The
coexistence region is extremely flat, attesting to an unusually small
tricritical exponent ; moreover, an extreme asymmetry of the phase
diagram is very striking. To accomodate this asymmetry, the second-order
boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR
An Analytic Equation of State for Ising-like Models
Using an Environmentally Friendly Renormalization we derive, from an
underlying field theory representation, a formal expression for the equation of
state, , that exhibits all desired asymptotic and analyticity
properties in the three limits , and . The only
necessary inputs are the Wilson functions , and
, associated with a renormalization of the transverse vertex
functions. These Wilson functions exhibit a crossover between the Wilson-Fisher
fixed point and the fixed point that controls the coexistence curve.
Restricting to the case N=1, we derive a one-loop equation of state for naturally parameterized by a ratio of non-linear scaling fields. For
we show that a non-parameterized analytic form can be deduced. Various
asymptotic amplitudes are calculated directly from the equation of state in all
three asymptotic limits of interest and comparison made with known results. By
positing a scaling form for the equation of state inspired by the one-loop
result, but adjusted to fit the known values of the critical exponents, we
obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond Blume-Capel model
The effects of bond randomness on the phase diagram and critical behavior of
the square lattice ferromagnetic Blume-Capel model are discussed. The system is
studied in both the pure and disordered versions by the same efficient
two-stage Wang-Landau method for many values of the crystal field, restricted
here in the second-order phase transition regime of the pure model. For the
random-bond version several disorder strengths are considered. We present phase
diagram points of both pure and random versions and for a particular disorder
strength we locate the emergence of the enhancement of ferromagnetic order
observed in an earlier study in the ex-first-order regime. The critical
properties of the pure model are contrasted and compared to those of the random
model. Accepting, for the weak random version, the assumption of the double
logarithmic scenario for the specific heat we attempt to estimate the range of
universality between the pure and random-bond models. The behavior of the
strong disorder regime is also discussed and a rather complex and yet not fully
understood behavior is observed. It is pointed out that this complexity is
related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio
Potts-Percolation-Gauss Model of a Solid
We study a statistical mechanics model of a solid. Neighboring atoms are
connected by Hookian springs. If the energy is larger than a threshold the
"spring" is more likely to fail, while if the energy is lower than the
threshold the spring is more likely to be alive. The phase diagram and
thermodynamic quantities, such as free energy, numbers of bonds and clusters,
and their fluctuations, are determined using renormalization-group and
Monte-Carlo techniques.Comment: 10 pages, 12 figure
Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation
The anisotropic XXZ spin-1/2 Heisenberg chain is studied using
renormalization-group theory. The specific heats and nearest-neighbor spin-spin
correlations are calculated thoughout the entire temperature and anisotropy
ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global
description and quantitative results. We obtain, for all anisotropies, the
antiferromagnetic spin-liquid spin-wave velocity and the Isinglike
ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon
crossover. A number of characteristics of purely quantum nature are found: The
in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic
correlation in the out-of-plane s_i^z component, at higher temperatures in the
antiferromagnetic XXZ chain, dominantly at low temperatures in the
ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain.
We find that the converse effect also occurs in the antiferromagnetic XXZ
chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in
the s_i^xy component. As another purely quantum effect, (i) in the
antiferromagnet, the value of the specific heat peak is insensitive to
anisotropy and the temperature of the specific heat peak decreases from the
isotropic (Heisenberg) with introduction of either type (Ising or XY)
anisotropy; (ii) in complete contrast, in the ferromagnet, the value and
temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3
tables. Published versio
Ordered phase and phase transitions in the three-dimensional generalized six-state clock model
We study the three-dimensional generalized six-state clock model at values of
the energy parameters, at which the system is considered to have the same
behavior as the stacked triangular antiferromagnetic Ising model and the
three-state antiferromagnetic Potts model. First, we investigate ordered phases
by using the Monte Carlo twist method (MCTM). We confirmed the existence of an
incompletely ordered phase (IOP1) at intermediate temperature, besides the
completely ordered phase (COP) at low-temperature. In this intermediate phase,
two neighboring states of the six-state model mix, while one of them is
selected in the low temperature phase. We examine the fluctuation the mixing
rate of the two states in IOP1 and clarify that the mixing rate is very stable
around 1:1.
The high temperature phase transition is investigated by using
non-equilibrium relaxation method (NERM). We estimate the critical exponents
beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY
universality class. The low temperature phase transition is found to be of
first-order by using MCTM and the finite-size-scaling analysis
Dynamic phase transition properties and hysteretic behavior of a ferrimagnetic core-shell nanoparticle in the presence of a time dependent magnetic field
We have presented dynamic phase transition features and stationary-state
behavior of a ferrimagnetic small nanoparticle system with a core-shell
structure. By means of detailed Monte Carlo simulations, a complete picture of
the phase diagrams and magnetization profiles have been presented and the
conditions for the occurrence of a compensation point in the system
have been investigated. According to N\'{e}el nomenclature, the magnetization
curves of the particle have been found to obey P-type, N-type and Q-type
classification schemes under certain conditions. Much effort has been devoted
to investigation of hysteretic response of the particle and we observed the
existence of triple hysteresis loop behavior which originates from the
existence of a weak ferromagnetic core coupling , as well as a
strong antiferromagnetic interface exchange interaction . Most
of the calculations have been performed for a particle in the presence of
oscillating fields of very high frequencies and high amplitudes in comparison
with exchange interactions which resembles a magnetic system under the
influence of ultrafast switching fields. Particular attention has also been
paid on the influence of the particle size on the thermal and magnetic
properties, as well as magnetic features such as coercivity, remanence and
compensation temperature of the particle. We have found that in the presence of
ultrafast switching fields, the particle may exhibit a dynamic phase transition
from paramagnetic to a dynamically ordered phase with increasing ferromagnetic
shell thickness.Comment: 12 pages, 12 figure
Symmetry Analysis of Barotropic Potential Vorticity Equation
Recently F. Huang [Commun. Theor. Phys. V.42 (2004) 903] and X. Tang and P.K.
Shukla [Commun. Theor. Phys. V.49 (2008) 229] investigated symmetry properties
of the barotropic potential vorticity equation without forcing and dissipation
on the beta-plane. This equation is governed by two dimensionless parameters,
and , representing the ratio of the characteristic length scale to
the Rossby radius of deformation and the variation of earth' angular rotation,
respectively. In the present paper it is shown that in the case there
exists a well-defined point transformation to set . The
classification of one- and two-dimensional Lie subalgebras of the Lie symmetry
algebra of the potential vorticity equation is given for the parameter
combination and . Based upon this classification, distinct
classes of group-invariant solutions is obtained and extended to the case
.Comment: 6 pages, release version, added reference for section
Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors
We present a functional renormalization group (FRG) analysis of a
Landau-Ginzburg model of type-II superconductors (generalized to complex
fields) in a magnetic field, both for a pure system, and in the presence of
quenched random impurities. Our analysis is based on a previous FRG treatment
of the pure case [E.Br\'ezin et. al., Phys. Rev. B, {\bf 31}, 7124 (1985)]
which is an expansion in . If the coupling functions are
restricted to the space of functions with non-zero support only at reciprocal
lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG
fixed point in the presence of disorder for , identical to that of the
disordered model in dimensions. The pure system has a stable fixed
point only for and so the physical case () is likely to have a
first order transition. We speculate that the recent experimental findings that
disorder removes the apparent first order transition are consistent with these
calculations.Comment: 4 pages, no figures, typeset using revtex (v3.0
Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks
In the reaction-diffusion process on random scale-free
(SF) networks with the degree exponent , the particle density decays
with time in a power law with an exponent when initial densities of
each species are the same. The exponent is for and for . Here, we examine the reaction
process on fractal SF networks, finding that even for . This slowly decaying behavior originates from the segregation effect:
Fractal SF networks contain local hubs, which are repulsive to each other.
Those hubs attract particles and accelerate the reaction, and then create
domains containing the same species of particles. It follows that the reaction
takes place at the non-hub boundaries between those domains and thus the
particle density decays slowly. Since many real SF networks are fractal, the
segregation effect has to be taken into account in the reaction kinetics among
heterogeneous particles.Comment: 4 pages, 6 figure
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