Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Employment, Production and Consumption model: Patterns of phase transitions

We have simulated the model of Employment, Production and Consumption (EPC) using Monte Carlo. The EPC model is an agent based model that mimics very basic rules of industrial economy. From the perspective of physics, the nature of the interactions in the EPC model represents multi-agent interactions where the relations among agents follow the key laws for circulation of capital and money. Monte Carlo simulations of the stochastic model reveal phase transition in the model economy. The two phases are the phase with full unemployment and the phase with nearly full employment. The economy switches between these two states suddenly as a reaction to a slight variation in the exogenous parameter, thus the system exhibits strong non-linear behavior as a response to the change of the exogenous parameters.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.     

A theoretical study of magnetic phase transitions in ultra-thin films: Application to NiO

Phase diagrams and critical temperatures of projected onto fcc (1 0 0) layers, which is believed to be applicable to first-row transition metal oxides such as VO, MnO and NiO, are obtained from mean field theory and Monte Carlo simulations. Within the regime, J_se > 0, which includes MnO and NiO, both approaches predict bicritical behaviour of the AF₂ and AF₃ antiferromagnetic spin alignments for odd numbers of layers greater than one and monocritical behaviour for even numbers of layers, even when films are described by single values of J_d and J_se. The ferromagnetic alignment, on the other hand, exhibits monocritical behaviour for all thicknesses from the monolayer through to the bulk. For values of (x = J_d/J_se) which are close to those obtained from first principles calculations for NiO and also those derived from measured magnon spectra, estimates of the thickness dependence of the critical temperature from Monte Carlo simulations are similar to that derived from linear polarised X-ray absorption spectra of NiO(1 0 0) ultra-thin films grown epitaxially on MgO(1 0 0) [D. Alders, L.H. Tjeng, F.C. Voogt, T. Hibma, G.A. Sawatzky, J. Vogel, M. Sacchi, S. Iacobucci, Phys. Rev. B 57 (1998) 11623].     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Identification of first- and second-order magnetic phase transitions in ferromagnetic perovskites

A criterion used for the determination of first- and second-order magnetic phase transitions from purely magnetic methods is applied to manganese perovskites of formula La_2/3(Ca_1−xSr_x)_1/3MnO₃. A crossover from first- to second-order character at a tolerance factor t=0.92 is found, which also brings about several variations in other physical properties. At t=0.92 a change from orthorhombic to rhombohedral symmetry also takes place. The impossibility of establishing static cooperative Jahn–Teller distortions in the rhombohedral symmetry is suggested as being responsible for the observed behaviour.     

Microkinetics of the first- and second-order phase transitions

A model of the phase transition in a lattice of interacting nodes, in which each node is a statistical system with internal structure, is introduced. Configuration entropy of microscopic states of the node is defined as a basic parameter of the model. In the frame of the model the first- and second-order phase transitions are considered in details. The distinction between them on the microscopic level is analyzed. Phase diagrams have been calculated in the mean-field approximation. Changes of the phase diagrams and modifications of phase transitions under external pressure and irradiation are investigated in the frame of the microkinetic approach. Results are referred to real systems.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

Nanophases in mechanochemically synthesized AgI-CuI system: structure, phase stability and phase transitions

Nanoscale crystallites of Ag-rich (Ag_1−xCu_xI, x=0.05, 0.10, 0.15 and 0.25), Cu-rich (Cu_1-yAg_yI, y=0.05, 0.10, 0.15 and 0.25) and intermediate Ag_1-xCu_xI (x=0.50) solid solutions and end members AgI, CuI with sizes in the range of 46-13 nm were synthesized by attrition at ambient temperature in a soft mechanochemical reaction (MCR) of Ag, Cu and I. Monophasic γ-AgI (zincblende, ) with disordered Ag⁺ sublattice and the crystallite size of about ∼31 nm was realized in the case of Ag_0.75Cu_0.25I (x=0.25) composition. Lattice parameter decreases linearly from 649 to 604 pm with increasing Cu concentration in the AgI-CuI system validating Vegard's law. Smallest size (∼13 nm) agglomerated nanocrystals were realized in the Cu-rich composition Cu_0.75Ag_0.25I (), while unagglomerated uniform-sized (∼17 nm) and spherical shape nanocrystallites of Ag_0.50Cu_0.50I () with maximum strain were synthesized for sensor applications using MCR. Differential scanning calorimetry study shows the systematic changes in the phase transition temperature with Cu substitution. Ag-rich composition posses less enthalpy (ΔH (x or Cu=0.05, 0.10, 0.15, 0.25)=6.0, 6.11, 6.6, 6.3 in kJ/mol) and entropy (ΔS (y or Ag=0.05, 0.10, 0.15, 0.25)=14.15, 14.1, 15.03, 13.6 in J/mol K) when compared to undoped AgI () implying greater thermal stability of γ-phase due to Cu-strengthened Ag-I bond. Enhanced entropy () in Cu_0.75Ag_0.25I (Cu-rich) solid solutions relative to CuI () indicates Ag-induced cation disorder. Fifteen percent Ag-doped CuI (Cu_0.85Ag_0.15I) nanocrystals apparently behave like microscopic p-n junctions with currents in the range of 10⁻⁶-10⁻⁸ A characterized by a non-linear I-V curve.     

Lyapunov exponents of stochastic dynamical systems

It is shown that stochastic equations can have stable solutions. In particular, there exists stochastic dynamics for which the motion is both ergodic and stable, so that all trajectories merge with time. We discuss this in the context of Monte Carlo-type dynamics, and study the convergence of nearby trajectories as the number of degrees of freedom goes to infinity and as a critical point is approached. A connection with critical slowdown is suggested.     

Dynamics and phase transitions in biased ladder systems with magnetic flux

The ground states and the dynamics of a biased two-leg flux ladder in the presence of a gravitational field are discussed. In the absence of the gravitational field, the ground states and the critical condition of phase transition are obtained analytically. We identify the Meissner phase, Vortex phase, and interestingly, two new Plane Wave phases, that break both $Z_2$ and time-reversal symmetry, characterized by the imbalance particle density distribution, asymmetry double well energy band structure in Plane Wave I (PWI) phase and asymmetry single well energy band structure in Plane Wave II (PWII) phase, respectively. In the presence of a longitudinal dc gravitational field, rich chiral Bloch oscillation and Landau-Zener tunneling are predicted theoretically and confirmed numerically. The characteristics of the chiral Bloch oscillation can distinguish the novel phases intuitively. Our work gives an interesting way to discuss the quantum phase transitions in a dynamical way.     

Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).     

Quantum phase transitions of spin chiral nanotubes

Recently many interesting magnetic nanostructures have been fabricated and much attention is arising on the rich magnetic properties that originate in the quantum effects eminent in the nanoscale world. One of the peculiar aspects of the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional systems, the spin gap often appears when the lattice dimerization or the frustration in the spin–spin interaction are introduced. In the present study, we investigate the ground-state property of the spin-1/2 antiferromagnetic spin chiral nanotubes with the spatial modulation in the spin–spin interaction. The ground-state phase diagrams of them are determined by observing the behavior of the expectation value of the Lieb–Schultz–Mattis slow-twist operator calculated by the quantum Monte Carlo method with the continuous-time loop algorithm. We discuss the relation between the characteristic of the topology of the phase diagram and the chiral vector of the nanotubes.     

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.Research supported by U.S. National Science Foundation under grants GP-40768X (F.J.D.), MCS 75-21684 (E.H.L.), and GP-39048 (B.S.).Alfred Sloan Fellow.     

Information geometry,phase transitions,and the Widom line: Magnetic and liquid systems

We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via a conjectured equality of the correlation lengths ξ$\xi$ in co-existing phases, where ξ$\xi$ is related to the scalar curvature of the equilibrium thermodynamic state space. The 1-D Ising model, and the mean-field Curie–Weiss model are discussed, and we show that information geometry correctly describes the phase behavior for the latter. The Widom lines for these systems are also established. We further study a toy model for the thermodynamics of liquid–liquid phase co-existence, and show that our method provides a simple and direct way to obtain its phase behavior and the location of the Widom line. Our analysis points towards the possibility of multiple Widom lines in liquid systems.     

About the poor decay of certain cross-correlation functions in the statistical mechanics of phase transitions in the static and dynamical regime

We introduce a method to prove poor decay of certain cross-correlation functions which are closely related to the phase transition. The methods apply both to equal and nonequal times, which gives access to the dynamical regime. We establish a criterion which displays openly what happens when the Goldstone picture breaks down. Since no rudiments of translation invariance are needed the treatment covers phases in coexistence like, e.g., liquid-gas interfaces and completely inhomogeneous systems. Furthermore a perhaps surprising connection with the breaking of time reflection invariance of the equilibrium state is established.     

Sequential desorption of dimers from square lattices: A novel mechanism for phase transitions

This work describes a novel mechanism for phase transitions during desorption, involving the formation of lattice size dependent intermediate states when there is enough adsorbate mobility. Monte Carlo simulations are performed to analyze the mechanism of the thermal desorption for adsorbed homonuclear dimers on two-dimensional square lattices. The lattice-gas model with nearest-neighbor repulsive interactions between particles is implemented to study the cases of mobile (with diffusion) and immobile desorption. The number of peaks for the immobile desorption spectra is related to the connectivity of the adsorbed species for both monomer and dimer molecules. However, for the case of mobile desorption, the spectra give information about the desorption mechanism, which differs significantly for monomers and dimers, particularly when the initial temperatures correspond to the critical region.     

First-order transitions in one-dimensional systems with local couplings

We point out the existence of first-order phase transitions in a family of one-dimensional classical spin systems. The relevant features of such models are that they involve only local (but complex) interactions and that the corresponding transfer matrices are self-adjoint operators. Moreover, for a wide range of coupling parameters the models satisfy the reflection positivity condition. The generalization for continuous spin systems enjoys similar properties.