Exact Ground-State Energy of the Ising Spin Glass on Strips

We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for complex values of the probability describing quenched randomness. We study the $\pm J$ and the site-random models using this method for strips of various sizes up to $5\times\infty$. The ground-state energy of these models is found to have singular points in the complex-probability plane, reminiscent of Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The $\pm J$ Ising model has a series of singularities which may approach a limiting point around $p \sim 0.9$ on the real axis in the limit of infinite width.Comment: 10 pages, 12 Postscript figures, LaTeX, uses subeqn.sty, minor changes in tex-fil

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

Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulas which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices. The examples include the +-J and Gaussian Ising spin glasses on the square, hexagonal and triangular lattices, the Potts and Z_q models with chiral randomness on these lattices, and the three-dimensional +-J Ising spin glass and the random plaquette gauge model.Comment: 27 pages, 3 figure

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

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 $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th moment of the spin overlap can be calculated as a simple average of the $n$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, $L$, 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 $10^{5}$ 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 $T_{\rm c}$ is strongly affected by the corrections to scaling within the present data ($L\leq 23$). Thus, there still remains the possibility that $T_{\rm c}=0$, 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.

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

Structural study of CHCl3 molecular assemblies in micropores using X-ray techniques

The original publication is available at www.springerlink.comArticleADSORPTION-JOURNAL OF THE INTERNATIONAL ADSORPTION SOCIETY. 11: 169-172 (2005)journal articl