1,209 research outputs found
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
Variation of the first Hilbert coefficients of parameters with a common integral closure
A problem posed by Wolmer V. Vasconcelos on the variation of the first
Hilbert coefficients of parameter ideals with a common integral closure in a
local ring is studied. Affirmative answers are given and counterexamples are
explored as well
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
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
Gauge Theory for Quantum Spin Glasses
The gauge theory for random spin systems is extended to quantum spin glasses
to derive a number of exact and/or rigorous results. The transverse Ising model
and the quantum gauge glass are shown to be gauge invariant. For these models,
an identity is proved that the expectation value of the gauge invariant
operator in the ferromagnetic limit is equal to the one in the classical
equilibrium state on the Nishimori line. As a result, a set of inequalities for
the correlation function are proved, which restrict the location of the ordered
phase. It is also proved that there is no long-range order in the
two-dimensional quantum gauge glass in the ground state. The phase diagram for
the quantum XY Mattis model is determined.Comment: 15 pages, 2 figure
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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