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. At 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.     

Dynamic phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

The stationary states of the kinetic spin-1 Blume-Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and crystal field (D) interactions. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. It is found that the magnetization oscillates around nonzero values at low temperatures (T) for the ferromagnetic (F) phase while it only oscillates around zero values at high temperatures for the paramagnetic (P) phase. There are regions of the phase space where the two solutions coexist. The dynamic phase diagrams are obtained on the (kT/J,h/J) and (kT/J,D/J) planes for the coordination number q=4. In addition to second-order and first-order phase transitions, dynamical tricritical points and triple points are also observed.     

Metal-insulator and magnetic phase transitions: A thermodynamic model

A thermodynamic model of magnetic insulator-to-metal transitions is presented. As the parameters are varied it shows with increasing temperatures; (a) antiferromagnetic insulator → paramagnetic insulator; or (b) antiferromagnetic insulator → metal → paramagnetic insulator; or (c) antiferromagnetic insulator → metal; or (d) metal at all temperatures. Behaviors (b) and (c) are separated by a classical critical point. The model reproduces well the behavior encounted in (V_1-xCr_x)₂O₃ and can be applied to magnetic semiconductors in general.     

Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

Physics of the Solid State - The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been...     

具有Dzyaloshinskii-Moriya作用的Blume-Capel模型的临界性质

应用二自旋集团平均场近似的方法,研究了蜂窝晶格和正方晶格上具有Dzyaloshinskii-Moriya(DM)作用的Blume-Capel模型的临界性质,得到了该系统的相图。结果表明,所研究系统存在三临界点,并且三临界温度不随DM作用参量单调变化,三临界温度有最小值。系统的这种临界性质是交换耦合作用、晶体场作用和DM作用三者相互竞争的结果。     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Mixed 2D molecular systems: Mechanic, thermodynamic and dielectric properties

Study of Langmuir monolayers consisting of stearic acid (SA) and dipalmitoylphosphatidylcholine (DPPC) molecules was done by surface pressure-area isotherms (π-A), the Maxwell displacement current (MDC) measurement, X-ray reflectivity (XRR) and atomic force microscopy (AFM) to investigate the selected mechanic, thermodynamic and dielectric properties based on orientational structure of monolayers. On the base of π-A isotherms analysis we explain the creation of stable structures and found optimal monolayer composition. The dielectric properties represented by MDC generated monolayers were analyzed in terms of excess dipole moment, proposing the effect of dipole-dipole interaction. XRR and AFM results illustrate deposited film structure and molecular ordering.     

Simple method for exact calculation of thermodynamic properties of the 1D Hubbard model with infinite repulsion

It is shown that the canonical partition function in the 1D Hubbard model with U = ∞ in the nearest neighbor approximation is determined by the product of canonical partition functions of spinons and holons. In this approximation, the concentration and temperature dependences of the free and internal energies, as well as of the chemical potential, entropy, and heat capacity, are calculated for electron concentrations of 0 ≤ n _e < 1.     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F₂) and three coexistence or mixed phase regions, namely the F₂+P, F₁+P and F₂+F₁+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.     

Percolation properties of the antiferromagnetic Blume-Capel model in the presence of a magnetic field

The problem of order-order and order-disorder transitions in the system described by the 2D antiferromagnetic Blume-Capel model in the presence of a magnetic field is studied by the Wang and Landau flat-histogram simulation method and by the classical Monte Carlo. Anomalous thermodynamic characteristics in low temperatures indicate different type orderings in finite temperatures. The existence of pure antiferromagnetic phases as well as mixed state is shown by detailed phenomenological analysis of the system. The border lines on the phase diagram between various orderings are determined by the complementary microscopic study of the percolation problem for c(2×2) elementary structures of antiferromagnetic ordered phases. This new approach has also shown a full agreement between the percolation threshold for the cluster of mixed phase and the critical temperature of the ordered system.     

Calculation of the thermodynamic properties of noble-metal alloys in the model electron-density functional method

The thermodynamic properties of the stable and metastable phases of theCu−Au, Ag−Au, andCu−Ag systems have been calculated in the representation of the many-body interatomic interaction potential within the framework of the model electron-density functional method. The calculated values of the thermodynamic properties are in good agreement with experimental data and help explain the laws of alloy formation in the given systems. Factors that affect the magnitude of the tetragonal distortion of theL1 ₀ structure of equiatomic alloys have been investigated. The possibility of a transition by the Bayne scheme from theL1 ₀ structure toB2 for alloyCuAu upon application of an external uniaxial [001] stress is discussed. Institute of Strength Physics and Materials Science, Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, p. 9–19, May, 1997.     

First-order phase transitions and integrable field theory. The dilute q-state Potts model

We consider the two-dimensional dilute q-state Potts model on its first-order phase transition surface for 0 < q ⩽ 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of the dilution, thermal and spin operators. They provide an approximation for the correlation functions whose accuracy is illustrated by evaluating the central charge and the scaling dimensions along the tricritical line.     

Orientational disordering in crystals—I: A model for the evaluation of thermodynamic properties of melting transitions in atomic and plastic crystals

A generalisation of two-sublattice models of melting transitions in atomic and molecular crystals (Lennard-Jones and Devonshire; Pople and Karasz; Amzel and Becka) has been attempted. The intention was to develop a scheme by which parameters, such as the number of sublattices and distinguishable molecular orientations can be selected. It is found that the choice of these parameters made by Lennard Jones and Devonshire, and by Pople and Karasz, protects the theory to some extent from some of the more difficult physical issues. A single-lattice model also emerges as another possibility in the series of models that may be called upon. Thus a single-lattice model, based on concepts from Eyring's Significant Structure Theory of Liquids for the melt, and standard thermodynamic functions for the solid, has been developed to evaluate thermodynamic properties of melting transitions in atomic and molecular crystals. Despite the remarkable simplicity of the model predicted values of entropy of fusion for both argon and methane are in good agreement with experimental data. Mean positional disordering energies for the same substances have also been computed.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).