194 research outputs found
A New Method to Calculate the Spin-Glass Order Parameter of the Two-Dimensional +/-J Ising Model
A new method to numerically calculate the th moment of the spin overlap of
the two-dimensional Ising model is developed using the identity derived
by one of the authors (HK) several years ago. By using the method, the th
moment of the spin overlap can be calculated as a simple average of the th
moment of the total spins with a modified bond probability distribution. The
values of the Binder parameter etc have been extensively calculated with the
linear size, , up to L=23. The accuracy of the calculations in the present
method is similar to that in the conventional transfer matrix method with about
bond samples. The simple scaling plots of the Binder parameter and the
spin-glass susceptibility indicate the existence of a finite-temperature
spin-glass phase transition. We find, however, that the estimation of is strongly affected by the corrections to scaling within the present data
(). Thus, there still remains the possibility that ,
contrary to the recent results which suggest the existence of a
finite-temperature spin-glass phase transition.Comment: 10 pages,8 figures: final version to appear in J. Phys.
Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line
The Griffiths inequalities for Ising spin glasses are proved on the Nishimori
line with various bond randomness which includes Gaussian and bond
randomness. The proof for Ising systems with Gaussian bond randomness has
already been carried out by Morita et al, which uses not only the gauge theory
but also the properties of the Gaussian distribution, so that it cannot be
directly applied to the systems with other bond randomness. The present proof
essentially uses only the gauge theory, so that it does not depend on the
detail properties of the probability distribution of random interactions. Thus,
the results obtained from the inequalities for Ising systems with Gaussian bond
randomness do also hold for those with various bond randomness, especially with
bond randomness.Comment: 13pages. Submitted to J. Phys. Soc. Jp
Criticality in the two-dimensional random-bond Ising model
The two-dimensional (2D) random-bond Ising model has a novel multicritical
point on the ferromagnetic to paramagnetic phase boundary. This random phase
transition is one of the simplest examples of a 2D critical point occurring at
both finite temperatures and disorder strength. We study the associated
critical properties, by mapping the random 2D Ising model onto a network model.
The model closely resembles network models of quantum Hall plateau transitions,
but has different symmetries. Numerical transfer matrix calculations enable us
to obtain estimates for the critical exponents at the random Ising phase
transition. The values are consistent with recent estimates obtained from
high-temperature series.Comment: minor changes, 7 pages LaTex, 8 postscript figures included using
epsf; to be published Phys. Rev. B 55 (1997
Surface Incommensurate Structure in an Anisotropic Model with competing interactions on Semiinfinite Triangular Lattice
An anisotropic spin model on a triangular semiinfinite lattice with
ferromagnetic nearest-neighbour interactions and one antiferromagnetic
next-nearest-neighbour interaction is investigated by the cluster
transfer-matrix method. A phase diagram with antiphase, ferromagnetic,
incommensurate, and disordered phase is obtained. The bulk uniaxial
incommensurate structure modulated in the direction of the competing
interactions is found between the antiphase and the disordered phase. The
incommensurate structure near the surface with free and boundary condition
is studied at different temperatures. Paramagnetic damping at the surface and
enhancement of the incommensurate structure in the subsurface region at high
temperatures and a new subsurface incommensurate structure modulated in two
directions at low temperatures are found.Comment: 13 pages, plainTex, 11 figures, paper submitted to J. Phys.
High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
We study the two and four dimensional Nishimori multicritical point via high
temperature expansions for the distribution, random-bond, Ising model.
In we estimate the the critical exponents along the Nishimori line to be
, . These, and earlier estimates
, are remarkably close to the critical
exponents for percolation, which are known to be , in
and and in . However, the
estimated Nishimori exponents , , are
quite distinct from the percolation results ,
.Comment: 5 pages, RevTex, 3 postscript files; To appear in Physical Review
Aging Relation for Ising Spin Glasses
We derive a rigorous dynamical relation on aging phenomena -- the aging
relation -- for Ising spin glasses using the method of gauge transformation.
The waiting-time dependence of the auto-correlation function in the
zero-field-cooling process is equivalent with that in the field-quenching
process. There is no aging on the Nishimori line; this reveals arguments for
dynamical properties of the Griffiths phase and the mixed phase. The present
method can be applied to other gauge-symmetric models such as the XY gauge
glass.Comment: 9 pages, RevTeX, 2 postscript figure
Finite Size Scaling of the 2D Six-Clock model
We investigate the isotropic-anisotropic phase transition of the
two-dimensional XY model with six-fold anisotropy, using Monte Carlo
renormalization group method. The result indicates difficulty of observing
asymptotic critical behavior in Monte Carlo simulations, owing to the marginal
flow at the fixed point.Comment: Short note. revtex, 6 pages, 3 figures. To appear in J. Phys. Soc.
Jpn. Vol.70 No. 2 (Feb 2001
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