186 research outputs found
Kosterlitz-Thouless Phase Transition of the ANNNI model in Two Dimensions
The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in
two dimensions (2D) is a renewed problem because different Monte Carlo (MC)
simulation methods predicted different spin orderings. The usual equilibrium
simulation predicts the occurrence of a floating incommensurate (IC)
Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium
relaxation (NER) simulations. In this paper, we first examine previously
published results of both methods, and then investigate a higher transition
temperature, , between the IC and paramagnetic phases. In the usual
equilibrium simulation, we calculate the layer magnetization on larger lattices
(up to sites) and estimate with
frustration ratio . We examine the nature of
the phase transition in terms of the Binder ratio of spin overlap
functions and the correlation-length ratio . In the NER simulation, we
observe the spin dynamics in equilibrium states by means of an autocorrelation
function, and also observe the layer magnetization relaxations from the ground
and disordered states. These quantities exhibit an algebraic decay at . We conclude that the two-dimensional ANNNI model actually
admits an IC phase transition of the KT type.Comment: 20 pages, 16 figure
Cluster Heat Bath Algorithm in Monte Carlo Simulations of Ising Models
We have proposed a cluster heat bath method in Monte Carlo simulations of
Ising models in which one of the possible spin configurations of a cluster is
selected in accordance with its Boltzmann weight. We have argued that the
method improves slow relaxation in complex systems and demonstrated it in an
axial next-nearest-neighbor Ising(ANNNI) model in two-dimensions.Comment: 10 pages, REVTeX, 2 figures, to appear in Phys.Rev.Let
Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy
We reexamine the spin glass (SG) phase transition of the Heisenberg
models with and without the random anisotropy in three dimensions ()
using complementary two methods, i.e., (i) the defect energy method and (ii)
the Monte Carlo method. We reveal that the conventional defect energy method is
not convincing and propose a new method which considers the stiffness of the
lattice itself. Using the method, we show that the stiffness exponent
has a positive value () even when . Considering the
stiffness at finite temperatures, we obtain the SG phase transition temperature
of for . On the other hand, a large scale MC
simulation shows that, in contrary to the previous results, a scaling plot of
the SG susceptibility for is obtained using almost the
same transiton temperature of . Hence we believe that
the SG phase transition occurs in the Heisenberg SG model in .Comment: 15 pages, 9 figures, to be published in J. Phys.
Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions
We have studied low-lying metastable states of the Heisenberg model
in two () and three () dimensions having developed a hybrid genetic
algorithm. We have found a strong evidence of the occurrence of the Parisi
states in but not in . That is, in lattices, there exist
metastable states with a finite excitation energy of for
, and energy barriers between the ground state and
those metastable states are with in
but with in . We have also found droplet-like
excitations, suggesting a mixed scenario of the replica-symmetry-breaking
picture and the droplet picture recently speculated in the Ising SG model.Comment: 4 pages, 6 figure
Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions
With the help of EXACT ground states obtained by a polynomial algorithm we
compute the domain wall energy at zero-temperature for the bond-random and the
site-random Ising spin glass model in two dimensions. We find that in both
models the stability of the ferromagnetic AND the spin glass order ceases to
exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the
vicinity of this critical point, the size and concentration dependency of the
first AND second moment of the domain wall energy are, for both models,
described by a COMMON finite size scaling form. Moreover, below this
concentration the stiffness exponent turns out to be slightly negative \theta_S
= -0.056(6) indicating the absence of any intermediate spin glass phase at
non-zero temperature.Comment: 7 pages Latex, 5 postscript-figures include
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.
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