9 research outputs found
Interfacial adsorption in two-dimensional pure and random-bond Potts models
No full textWe use Monte Carlo simulations to study the finite-size scaling behavior of the interfacial adsorption of the two-dimensional square-lattice q-states Potts model. We consider the pure and random-bond versions of the Potts model for q=3,4,5,8, and 10, thus probing the interfacial properties at the originally continuous, weak, and strong first-order phase transitions. For the pure systems our results support the early scaling predictions for the size dependence of the interfacial adsorption at both first- and second-order phase transitions. For the disordered systems, the interfacial adsorption at the (disordered induced) continuous transitions is discussed, applying standard scaling arguments and invoking findings for bulk critical properties. The self-averaging properties of the interfacial adsorption are also analyzed by studying the infinite limit-size extrapolation of properly defined signal-to-noise ratios
Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
No full textWe investigate the dependence of the critical Binder cumulant of the magnetization and the largest Fortuin- Kasteleyn cluster on the boundary conditions and aspect ratio of the underlying square Ising lattices. By means of the Swendsen-Wang algorithm, we generate numerical data for large system sizes and we perform a detailed finite-size scaling analysis for several values of the aspect ratio r, for both periodic and free boundary conditions. We estimate the universal probability density functions of the largest Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at criticality. It is shown that these probability density functions follow similar scaling laws, and it is found that the values of the critical Binder cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the values of the respective order-parameter’s cumulant, with a splitting behavior for large values of the aspect ratio.We also investigate the dependence of the amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on the aspect ratio and boundary conditions. We find that the associated exponents, describing the aspect-ratio dependencies, are different for the magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are independent of boundary conditions
Interfacial adsorption in Potts models on the square lattice
No full textWe study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) q-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., q = 3, 4, and q = 8, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point
Monte Carlo study of the interfacial adsorption of the Blume-Capel model
No full textWe investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model
Multicanonical simulations of the 2D spin-1 Baxter-Wu model in a crystal field
No full textWe investigate aspects of universality in the two-dimensional (2D) spin-1 Baxter- Wu model in a crystal field ∆ using a parallel version of the multicanonical algorithm employed at constant temperature T . A detailed finite-size scaling analysis in the continuous regime of the ∆ − T phase diagram of the model indicates that the transition belongs to the universality class of the 4-state Potts model. The presence of first-order-like finite-size effects that become more pronounced as one approaches the pentacritical point of the model is highlighted and discussed
Critical aspects of three-dimensional anisotropic spin-glass models
No full textWe study the three-dimensional ± J Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the z direction, whereas in the other two directions, xy-planes, we consider ferromagnetic exchange. By implementing an effective parallel tempering scheme, we outline the phase diagram of the model and compare it to the corresponding isotropic one. We present a detailed finite-size scaling analysis of the ferromagnetic-paramagnetic and spin glass-paramagnetic transition lines, and we also discuss the ferromagnetic-spin glass transition regime. We conclude that the present model shares the same universality classes with the isotropic model, but at the symmetric point has a considerably higher transition temperature from the spin-glass state to the paramagnetic phase. Our data for the ferromagnetic-spin glass transition line support a forward behavior in contrast to the reentrant behavior of the corresponding isotropic model
Scaling and universality in the phase diagram of the 2D Blume-Capel model
No full textWe review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of with the exactly known result for the Ising universality class.Publisher Statement: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60337-
Universality in the two-dimensional dilute Baxter-Wu model
No full textWe study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model
The Greek Dream by Monsieur de Choiseul: The Travels of a European of the Enlightenment. [Review of the Book: Le rêve grec de Monsieur de Choiseul Les voyages d'un européen des Lumières by Frédéric Barbier]
No full textFrédéric Barbier takes us on a long journey, that of a French aristocrat of the Age of Enlightenment, "a man with a dream," a vision of a Europe in the process of construction, inspired by a "Greek antiquity not only idealized but accomplishable in modernity" (15). Barbier offers us a biography on a figure of the first generation of French Philhellenism. Biographies of male and female travel writers of the past centuries are extremely rare, such as Sture Linnér's (1965) book on nineteenth century Swedish traveler Fredrika Bremer i Grekland (Frederika Bremer in Greece), translated and published in Greek in 1997. Barbier provides the first biography of Count Marie-Gabriel-Florent-Auguste de Choiseul-Gouffier (1752–1817; henceforth, Choiseul), a fervent admirer of ancient Greek civilization. Barbier's book consists of nine chapters, in addition to the author's acknowledgements (11–12), an epilogue (269–275), and a portrait of Choiseul (277), followed by a bibliographical appendix (279–286), an index (287–297), and a table of 40 illustrations (299–300) from Voyage pittoresque de la Grèce, which include three illustrations of the women of Sifnos (105), Tinos (144), and Constantinople (265). By focusing on one specific traveler, here a French aristocrat during the Enlightenment, Barbier contributes to the research of other scholars on Philhellenism, while also shedding light on the spirit of the time. Through the travel accounts of Choiseul—Le voyage pittoresque de la Grèce (published in three volumes in 1782, 1809, and 1824)—Barbier illustrates the major social changes marking the end of the eighteenth and beginning of the nineteenth centuries: the French Revolution, Napoleon as First Council, the Congress of Vienna and Treaty of Paris, the Conservative Order and Counter-Enlightenment, the uprisings in Greece, and so forth. The intense concern of France in the affairs of the Near East and the imminence of the liberation of the Greeks is brought out by many travelers like Charles Nicolas Sigisbert Sonnini [End Page 564] de Manoncourt (1751–1812), a French nobleman, in his publication Voyage en Grèce et en Turquie (Sonnini 1801). During this period of social and political transformations, many western travelers like Choiseul visited and explored Greece—and not only for pleasure, profit, and culture. American and European volunteers participated in the struggle for Greek independence, producing, among other things, a body of travel writing about Greece (Larrabee 1957). Philhellenism in France had reached its peak during the Greek insurrection between the years 1820 and 1830, as illustrated in Emile Malakis's dissertation (1925) on French travelers to Greece from 1770 to 1820
