Recent Progress in Spin Glasses

We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.Comment: Chapter 6 in ``Frustrated Spin Systems'' edited by H.T.Die

Application of a continous time cluster algorithm to the Two-dimensional Random Quantum Ising Ferromagnet

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d.Comment: 4 pages RevTeX, 3 eps-figures include

Double-q\it q Order in a Frustrated Random Spin System

We use the three-dimensional Heisenberg model with site randomness as an effective model of the compound Sr(Fe$_{1-x}$Mn$_x$)O$_2$. The model consists of two types of ions that correspond to Fe and Mn ions. The nearest-neighbor interactions in the ab-plane are antiferromagnetic. The nearest-neighbor interactions along the c-axis between Fe ions are assumed to be antiferromagnetic, whereas other interactions are assumed to be ferromagnetic. From Monte Carlo simulations, we confirm the existence of the double-$\boldsymbol{q}$ ordered phase characterized by two wave numbers, $(\pi\pi\pi)$ and $(\pi\pi0)$. We also identify the spin ordering pattern in the double-$\boldsymbol{q}$ ordered phase.Comment: 5pages, 3figure

Statistical mechanics and large-scale velocity fluctuations of turbulence

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/

Numerical renormalization group study of random transverse Ising models in one and two space dimensions

The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the analytically tractable one-dimensional case and apply our code to the quasi-one-dimensional double chain. For the latter we obtain identical critical exponents as for the simple chain implying the same universality class. Then we apply the method to the two-dimensional case for which we get estimates for the exponents that are compatible with a recent study in the same spirit.Comment: 10 pages LaTeX, eps-figures and PTP-macros included. Proceedings of the ICCP5, Kanazawa (Japan), 199

Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with $S=1$, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy

Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions

By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.Comment: 19 pages with 9 postscript figures also available at http://chimera.roma1.infn.it/index_papers_complex.html. Some changes in captions of figures 1 and

Numerical study of the ordering of the +-J XY spin-glass ladder

The properties of the domain-wall energy and of the correlation length are studied numerically for the one-dimensional +-J XY spin glass on the two-leg ladder lattice, focusing on both the spin and the chirality degrees of freedom. Analytic results obtained by Ney-Niftle et al for the same model were confirmed for asymptotically large lattices, while the approach to the asymptotic limit is slow and sometimes even non-monotonic. Attention is called to the occurrence of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is given concerning the behaviors of the higher-dimensional models.Comment: 14 pages, 10 figure

Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.Comment: 48 pages 14 figures RevTe

Dual Monte Carlo and Cluster Algorithms

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.