Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999

Zero-variance principle for Monte Carlo algorithms

We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.Comment: 9 pages, Latex, to appear in Phys. Rev. Let

Simulation of Potts models with real q and no critical slowing down

A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes a random value to the link, regardless of the state of the system, while in a deterministic move this value is a state function. The relative frequency of these moves depends on the two parameters q and beta. The algorithm is not affected by critical slowing down and the dynamical critical exponent z is exactly vanishing. We simulate in this way a 3D Potts model in the range 2<q<3 for estimating the critical value q_c where the thermal transition changes from second-order to first-order, and find q_c=2.620(5).Comment: 5 pages, 3 figures slightly extended version, to appear in Phys. Rev.

Quantum Monte Carlo Loop Algorithm for the t-J Model

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local algorithms. The method is completely ergodic and can be formulated directly in continuous time. We introduce improved estimators for simulations with a local sign problem. Some first results of finite temperature simulations are presented for a t-J chain, a frustrated Heisenberg chain, and t-J ladder models.Comment: 22 pages, including 12 figures. RevTex v3.0, uses psf.te

Changes in the relationship between self-reference and emotional valence as a function of dysphoria

The self-positivity bias is found to be an aspect of normal cognitive function. Changes in this bias are usually associated with changes in emotional states, such as dysphoria or depression. The aim of the present study was to clarify the role of emotional valence within self-referential processing. By asking non-dysphoric and dysphoric individuals to rate separately the emotional and self-referential content of a set of 240 words, it was possible to identify the differences in the relationship between self-reference and emotional valence, which are associated with dysphoria. The results support the existence of the self-positivity bias in non-dysphoric individuals. More interestingly, dysphoric individuals were able to accurately identify the emotional content of the word stimuli. They failed, however, to associate this emotional valence with self-reference. These findings are discussed in terms of attributional self-biases and their consequences for cognition

Auger Recombination in Semiconductor Quantum Wells

The principal mechanisms of Auger recombination of nonequilibrium carriers in semiconductor heterostructures with quantum wells are investigated. It is shown for the first time that there exist three fundamentally different Auger recombination mechanisms of (i) thresholdless, (ii) quasi-threshold, and (iii) threshold types. The rate of the thresholdless Auger process depends on temperature only slightly. The rate of the quasi-threshold Auger process depends on temperature exponentially. However, its threshold energy essentially varies with quantum well width and is close to zero for narrow quantum wells. It is shown that the thresholdless and the quasi-threshold Auger processes dominate in narrow quantum wells, while the threshold and the quasi-threshold processes prevail in wide quantum wells. The limiting case of a three-dimensional (3D)Auger process is reached for infinitely wide quantum wells. The critical quantum well width is found at which the quasi-threshold and threshold Auger processes merge into a single 3D Auger process. Also studied is phonon-assisted Auger recombination in quantum wells. It is shown that for narrow quantum wells the act of phonon emission becomes resonant, which in turn increases substantially the coefficient of phonon-assisted Auger recombination. Conditions are found under which the direct Auger process dominates over the phonon-assisted Auger recombination at various temperatures and quantum well widths.Comment: 38 pages, 7 figure

The Percolation Signature of the Spin Glass Transition

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the $\pm J$ EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {\it two} percolating clusters of {\it unequal} densities.Comment: 13 pages, 6 figure

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process

A Percolation-Theoretic Approach to Spin Glass Phase Transitions

The magnetically ordered, low temperature phase of Ising ferro- magnets is manifested within the associated Fortuin-Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering -- both in the short-range Edwards-Anderson (EA) and infinite-range Sherrington-Kirkpatrick (SK) models -- within a two-replica FK representation and also in the different Chayes-Machta-Redner two-replica graphical representation. Numerical studies of the $\pm J$ EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that the signature of spin-glass order in these models is the existence of a single percolating cluster of maximal density normally coexisting with a second percolating cluster of lower density.Comment: Based on lectures given at the 2007 Paris Summer School "Spin Glasses." 12 pages, 3 figure