457 research outputs found
Universality aspects of the d=3 random-bond Blume-Capel model
The effects of bond randomness on the universality aspects of the simple
cubic lattice ferromagnetic Blume-Capel model are discussed. The system is
studied numerically in both its first- and second-order phase transition
regimes by a comprehensive finite-size scaling analysis. We find that our data
for the second-order phase transition, emerging under random bonds from the
second-order regime of the pure model, are compatible with the universality
class of the 3d random Ising model. Furthermore, we find evidence that, the
second-order transition emerging under bond randomness from the first-order
regime of the pure model, belongs to a new and distinctive universality class.
The first finding reinforces the scenario of a single universality class for
the 3d Ising model with the three well-known types of quenched uncorrelated
disorder (bond randomness, site- and bond-dilution). The second, amounts to a
strong violation of universality principle of critical phenomena. For this case
of the ex-first-order 3d Blume-Capel model, we find sharp differences from the
critical behaviors, emerging under randomness, in the cases of the
ex-first-order transitions of the corresponding weak and strong first-order
transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure
Uncovering the secrets of the 2d random-bond Blume-Capel model
The effects of bond randomness on the ground-state structure, phase diagram
and critical behavior of the square lattice ferromagnetic Blume-Capel (BC)
model are discussed. The calculation of ground states at strong disorder and
large values of the crystal field is carried out by mapping the system onto a
network and we search for a minimum cut by a maximum flow method. In finite
temperatures the system is studied by an efficient two-stage Wang-Landau (WL)
method for several values of the crystal field, including both the first- and
second-order phase transition regimes of the pure model. We attempt to explain
the enhancement of ferromagnetic order and we discuss the critical behavior of
the random-bond model. Our results provide evidence for a strong violation of
universality along the second-order phase transition line of the random-bond
version.Comment: 6 LATEX pages, 3 EPS figures, Presented by AM at the symposium
"Trajectories and Friends" in honor of Nihat Berker, MIT, October 200
High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows
The recently developed tensor renormalization-group (TRG) method provides a
highly precise technique for deriving thermodynamic and critical properties of
lattice Hamiltonians. The TRG is a local coarse-graining transformation, with
the elements of the tensor at each lattice site playing the part of the
interactions that undergo the renormalization-group flows. These tensor flows
are directly related to the phase diagram structure of the infinite system,
with each phase flowing to a distinct surface of fixed points. Fixed-point
analysis and summation along the flows give the critical exponents, as well as
thermodynamic functions along the entire temperature range. Thus, for the
ferromagnetic triangular lattice Ising model, the free energy is calculated to
better than 10^-5 along the entire temperature range. Unlike previous
position-space renormalization-group methods, the truncation (of the tensor
index range D) in this general method converges under straightforward and
systematic improvements. Our best results are easily obtained with D = 24,
corresponding to 4624-dimensional renormalization-group flows.Comment: 6 pages, 5 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
Exact solution of mean geodesic distance for Vicsek fractals
The Vicsek fractals are one of the most interesting classes of fractals and
the study of their structural properties is important. In this paper, the exact
formula for the mean geodesic distance of Vicsek fractals is found. The
quantity is computed precisely through the recurrence relations derived from
the self-similar structure of the fractals considered. The obtained exact
solution exhibits that the mean geodesic distance approximately increases as an
exponential function of the number of nodes, with the exponent equal to the
reciprocal of the fractal dimension. The closed-form solution is confirmed by
extensive numerical calculations.Comment: 4 pages, 3 figure
Random site dilution properties of frustrated magnets on a hierarchical lattice
We present a method to analyze magnetic properties of frustrated Ising spin
models on specific hierarchical lattices with random dilution. Disorder is
induced by dilution and geometrical frustration rather than randomness in the
internal couplings of the original Hamiltonian. The two-dimensional model
presented here possesses a macroscopic entropy at zero temperature in the large
size limit, very close to the Pauling estimate for spin-ice on pyrochlore
lattice, and a crossover towards a paramagnetic phase. The disorder due to
dilution is taken into account by considering a replicated version of the
recursion equations between partition functions at different lattice sizes. An
analysis at first order in replica number allows for a systematic
reorganization of the disorder configurations, leading to a recurrence scheme.
This method is numerically implemented to evaluate the thermodynamical
quantities such as specific heat and susceptibility in an external field.Comment: 26 pages, 11 figure
Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory
The global phase diagram of the spinless Falicov-Kimball model in d = 3
spatial dimensions is obtained by renormalization-group theory. This global
phase diagram exhibits five distinct phases. Four of these phases are
charge-ordered (CO) phases, in which the system forms two sublattices with
different electron densities. The CO phases occur at and near half filling of
the conduction electrons for the entire range of localized electron densities.
The phase boundaries are second order, except for the intermediate and large
interaction regimes, where a first-order phase boundary occurs in the central
region of the phase diagram, resulting in phase coexistence at and near half
filling of both localized and conduction electrons. These two-phase or
three-phase coexistence regions are between different charge-ordered phases,
between charge-ordered and disordered phases, and between dense and dilute
disordered phases. The second-order phase boundaries terminate on the
first-order phase transitions via critical endpoints and double critical
endpoints. The first-order phase boundary is delimited by critical points. The
cross-sections of the global phase diagram with respect to the chemical
potentials and densities of the localized and conduction electrons, at all
representative interactions strengths, hopping strengths, and temperatures, are
calculated and exhibit ten distinct topologies.Comment: Calculated density phase diagrams. Added discussions and references.
14 pages, 9 figures, 4 table
Real-space renormalization group for the random-field Ising model
We present real--space renormalization group (RG) calculations of the
critical properties of the random--field Ising model on a cubic lattice in
three dimensions. We calculate the RG flows in a two--parameter truncation of
the Hamiltonian space. As predicted, the transition at finite randomness is
controlled by a zero temperature, disordered critical fixed point, and we
exhibit the universal crossover trajectory from the pure Ising critical point.
We extract scaling fields and critical exponents, and study the distribution of
barrier heights between states as a function of length scale.Comment: 12 pages, CU-MSC-757
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
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