1,903 research outputs found
Phase Diagram of a 2D Vertex Model
Phase diagram of a symmetric vertex model which allows 7 vertex
configurations is obtained by use of the corner transfer matrix renormalization
group (CTMRG), which is a variant of the density matrix renormalization group
(DMRG). The critical indices of this model are identified as and
.Comment: 2 pages, 5 figures, short not
Critical Point of a Symmetric Vertex Model
We study a symmetric vertex model, that allows 10 vertex configurations, by
use of the corner transfer matrix renormalization group (CTMRG), a variant of
DMRG. The model has a critical point that belongs to the Ising universality
class.Comment: 2 pages, 6 figures, short not
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
We report a way of obtaining a spin configuration snapshot, which is one of
the representative spin configurations in canonical ensemble, in a finite area
of infinite size two-dimensional (2D) classical lattice models. The corner
transfer matrix renormalization group (CTMRG), a variant of the density matrix
renormalization group (DMRG), is used for the numerical calculation. The matrix
product structure of the variational state in CTMRG makes it possible to
stochastically fix spins each by each according to the conditional probability
with respect to its environment.Comment: 4 pages, 8figure
Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models
We develop a new variant of the recently introduced stochastic
transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix
DMRG (LCTMRG). It is a numerical method to compute dynamic properties of
one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a
modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an
additional causality argument. As an example, two reaction-diffusion models,
the diffusion-annihilation process and the branch-fusion process, are studied
and compared to exact data and Monte-Carlo simulations to estimate the
capability and accuracy of the new method. The number of possible Trotter steps
of more than 10^5 shows a considerable improvement to the old stochastic TMRG
algorithm.Comment: 15 pages, uses IOP styl
Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
Critical behavior of the Ising model is investigated at the center of large
scale finite size systems, where the lattice is represented as the tiling of
pentagons. The system is on the hyperbolic plane, and the recursive structure
of the lattice makes it possible to apply the corner transfer matrix
renormalization group method. From the calculated nearest neighbor spin
correlation function and the spontaneous magnetization, it is concluded that
the phase transition of this model is mean-field like. One parameter
deformation of the corner Hamiltonian on the hyperbolic plane is discussed.Comment: 4 pages, 5 figure
Non-Abelian Tensors with Consistent Interactions
We present a systematic method for constructing consistent interactions for a
tensor field of an arbitrary rank in the adjoint representation of an arbitrary
gauge group in any space-time dimensions. This method is inspired by the
dimensional reduction of Scherk-Schwarz, modifying field strengths with certain
Chern-Simons forms, together with modified tensorial gauge transformations. In
order to define a consistent field strength of a r-rank tensor
B_{\mu_1...\mu_r}^I in the adjoint representation, we need the multiplet
(B_{\mu_1...\mu_r}^I, B_{\mu_1...\mu_{r-1}}^{I J}, ..., B_\mu^{I_1...I_r},
B^{I_1... I_{r+1}}). The usual problem of consistency of the tensor field
equations is circumvented in this formulation.Comment: 15 pages, no figure
Incommensurate structures studied by a modified Density Matrix Renormalization Group Method
A modified density matrix renormalization group (DMRG) method is introduced
and applied to classical two-dimensional models: the anisotropic triangular
nearest- neighbor Ising (ATNNI) model and the anisotropic triangular
next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have
complex structures and exhibit incommensurate phases. It was found that the
incommensurate phase completely separates the disordered phase from one of the
commensurate phases, i. e. the non-existence of the Lifshitz point in phase
diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB,
presented at MECO'24 1999 (Wittenberg, Germany
Phase Transition of the Ising model on a Hyperbolic Lattice
The matrix product structure is considered on a regular lattice in the
hyperbolic plane. The phase transition of the Ising model is observed on the
hyperbolic lattice by means of the corner-transfer-matrix
renormalization group (CTMRG) method. Calculated correlation length is always
finite even at the transition temperature, where mean-field like behavior is
observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure
Censoring Distances Based on Labeled Cortical Distance Maps in Cortical Morphometry
Shape differences are manifested in cortical structures due to
neuropsychiatric disorders. Such differences can be measured by labeled
cortical distance mapping (LCDM) which characterizes the morphometry of the
laminar cortical mantle of cortical structures. LCDM data consist of signed
distances of gray matter (GM) voxels with respect to GM/white matter (WM)
surface. Volumes and descriptive measures (such as means and variances) for
each subject and the pooled distances provide the morphometric differences
between diagnostic groups, but they do not reveal all the morphometric
information contained in LCDM distances. To extract more information from LCDM
data, censoring of the distances is introduced. For censoring of LCDM
distances, the range of LCDM distances is partitioned at a fixed increment
size; and at each censoring step, and distances not exceeding the censoring
distance are kept. Censored LCDM distances inherit the advantages of the pooled
distances. Furthermore, the analysis of censored distances provides information
about the location of morphometric differences which cannot be obtained from
the pooled distances. However, at each step, the censored distances aggregate,
which might confound the results. The influence of data aggregation is
investigated with an extensive Monte Carlo simulation analysis and it is
demonstrated that this influence is negligible. As an illustrative example, GM
of ventral medial prefrontal cortices (VMPFCs) of subjects with major
depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy
control (Ctrl) subjects are used. A significant reduction in laminar thickness
of the VMPFC and perhaps shrinkage in MDD and HR subjects is observed when
compared to Ctrl subjects. The methodology is also applicable to LCDM-based
morphometric measures of other cortical structures affected by disease.Comment: 25 pages, 10 figure
- …