Field-Driven Hysteresis of the d=3 Ising Spin Glass: Hard-Spin Mean-Field Theory

Hysteresis loops are obtained in the Ising spin-glass phase in d=3, using frustration-conserving hard-spin mean-field theory. The system is driven by a time-dependent random magnetic field H_Q that is conjugate to the spin-glass order Q, yielding a field-driven first-order phase transition through the spin-glass phase. The hysteresis loop area A of the Q-H_Q curve scales with respect to the sweep rate h of magnetic field as A-A_0 = h^b. In the spin-glass and random-bond ferromagnetic phases, the sweep-rate scaling exponent b changes with temperature T, but appears not to change with antiferromagnetic bond concentration p. By contrast, in the pure ferromagnetic phase, b does not depend on T and has a sharply different value than in the two other phases.Comment: 5 pages, 8 figures, 1 table. Replaced with published versio

Universality aspects of the d=3 random-bond Blume-Capel model

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure

Uncovering the secrets of the 2d random-bond Blume-Capel model

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. In finite temperatures the system is studied by an efficient two-stage Wang-Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.Comment: 6 LATEX pages, 3 EPS figures, Presented by AM at the symposium "Trajectories and Friends" in honor of Nihat Berker, MIT, October 200

Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond d=2d=2 Blume-Capel model

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.Comment: 12 pages, 11 figures, submitted for publicatio

Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness

We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the 2d Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with \nu=1.30(6) and \beta/\nu=0.128(5). This amounts to a strong violation of the universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two transitions supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.Comment: Added discussion and references. 10 pages, 6 figures. Published versio

Deep Spin-Glass Hysteresis Area Collapse and Scaling in the d=3d=3 ±J\pm J Ising Model

We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate, by means of frustration-preserving hard-spin mean field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely-slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency $\omega_c$ characterize the dependence on the sweep rate of the oscillating field. For $\omega < \omega_c$, the hysteresis area is equal to its value in the adiabatic limit $\omega = 0$, while for $\omega > \omega_c$ it increases with the frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure

Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation

The anisotropic XXZ spin-1/2 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated thoughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Isinglike ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic correlation in the out-of-plane s_i^z component, at higher temperatures in the antiferromagnetic XXZ chain, dominantly at low temperatures in the ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain. We find that the converse effect also occurs in the antiferromagnetic XXZ chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in the s_i^xy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XY) anisotropy; (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3 tables. Published versio

On the Error Probability of Cognitive RF-FSO Relay Networks over Rayleigh/EW Fading Channels with Primary-Secondary Interference

Free space optical (FSO) communication has emerged to provide line of sight connectivity and higher throughput over unlicensed optical spectrums. Cognitive radio (CR), on the other hand, can utilize the radio frequency (RF) spectrum and allow a secondary user (SU) to share the same spectrum with the primary user (PU) as long as the SU does not impose interference on the PU. Owing to the potential of these emerging technologies, to provide full spectrum efficiency, this paper focuses on the mixed CR RF-FSO transmission scheme, where RF communication is employed at one hop followed by the FSO transmission on the other hop in a dual-hop decode-and-forward (DF) configuration. To quantify the performance of the propose

Strongly Asymmetric Tricriticality of Quenched Random-Field Systems

In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random fields on the tricritical phase diagram of the spin-1 Ising model in $d=3$. We find that random fields convert first-order phase transitions into second-order, in fact more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent $\beta_u$; moreover, an extreme asymmetry of the phase diagram is very striking. To accomodate this asymmetry, the second-order boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR

Non-Standard Intersections of S-Branes in D=11 Supergravity

We construct new intersecting S-brane solutions in 11-dimensional supergravity which do not have supersymmetric analogs. They are obtained by letting brane charges to be proportional to each other. Solutions fall into two categories with respect to whether there is a non-diagonal term to be cancelled in the field equations or not. In each case we show that they can be constructed by using a simple set of rules which is similar to the harmonic function rule of the usual static p-branes. Furthermore, we study an intersection where the Chern-Simons term makes a non-zero contribution to the field equations. We show that this configuration has a singularity like other S-branes.Comment: 13 pages, 2 figures;v2 Section 2.2 is improved with new examples, references added;v3 typos correcte