Dynamic phase transition of the Blume-Capel model in an oscillating magnetic field

Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017)0031-900710.1103/PhysRevLett.118.117202; G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)2469-995010.1103/PhysRevB.96.134306]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)0163-182910.1103/PhysRevB.34.1797]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.

Critical dynamics of cluster algorithms in the random-bond Ising model

In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.

Metamagnetic fluctuation characteristics near dynamic phase transitions

We experimentally explore the magnetization dynamics of thin ferromagnetic Co films with uniaxial in-plane anisotropy near the dynamic phase transition (DPT) and, in particular, we study the temporal characteristics of anomalous metamagnetic fluctuations that occur in its vicinity, and for which no thermodynamic equivalent exists. For this purpose, we measure the real-time evolution of magnetization trajectories in the relevant dynamic phase space, conduct a Fourier analysis of these experimental results and compare it to a model, in which the fluctuating metamagnetic behavior occurs in a purely random manner, following individual state probability distributions. We find excellent quantitative agreement in between our experimental results and the random state model, clearly indicating that multiperiod time-correlations of magnetic states are not relevant in our DPT system, not even for the occurrence of the anomalous metamagnetic fluctuations that are nonetheless associated with nonperiodic magnetic state evolutions.

Experimental Observation of Critical Scaling in Magnetic Dynamic Phase Transitions

We explore the critical behavior of dynamic phase transitions in ultrathin uniaxial Co films. Our data demonstrate the occurrence of critical fluctuations, which define the critical regime, and in which we conduct a scaling analysis of the dynamic order parameter Q, utilizing a dynamic analog to the Arrott-Noakes equation of state. Our results show dynamic critical exponents that agree with the 2D Ising model as theoretically predicted. However, equilibrium critical exponents of our sample agree with the 3D Ising model. We argue that these differences between dynamic and thermodynamic behavior are due to fundamentally different length scales at which dimensional crossovers occur.

Exploring the equilibrium and dynamic phase transition properties of the Ising ferromagnet on a decorated triangular lattice

We study the equilibrium and dynamic phase transition properties of a two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time-independent bias term. Using Monte Carlo simulations with a standard Metropolis algorithm, we determine the equilibrium critical behavior in zero field. At a fixed temperature corresponding to the multidroplet regime, we locate the relaxation time and the dynamic critical half period at which a dynamic phase transition takes place between ferromagnetic and paramagnetic states. Benefiting from finite-size scaling theory, we estimate the dynamic critical exponent ratios for the dynamic order parameter and its scaled variance, respectively. The response function of the average energy is found to follow a logarithmic scaling as a function of lattice size. At the critical half period and in the vicinity of a small bias field regime, the average of the dynamic order parameter obeys a scaling relation with a dynamic scaling exponent which is very close to the equilibrium critical isotherm value. Finally, in the slow critical dynamics regime, investigation of metamagnetic fluctuations in the presence of bias field reveals a symmetric double-peak behavior for the scaled variance contours of the dynamic order parameter and average energy. Our results strongly resemble those previously reported for kinetic Ising models.

Dynamic phase transitions on the kagome Ising ferromagnet

We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.

Monte Carlo study of the two-dimensional kinetic Blume-Capel model in a quenched random crystal field

We investigate by means of Monte Carlo simulations the dynamic phase transition of the two-dimensional kinetic Blume-Capel model under a periodically oscillating magnetic field in the presence of a quenched random crystal-field coupling. We analyze the universality principles of this dynamic transition for various values of the crystal-field coupling at the originally second-order regime of the corresponding equilibrium phase diagram of the model. A detailed finite-size scaling analysis indicates that the observed nonequilibrium phase transition belongs to the universality class of the equilibrium Ising ferromagnet with additional logarithmic corrections in the scaling behavior of the heat capacity. Our results are in agreement with earlier works on kinetic Ising models.

On Markov blankets and hierarchical self-organisation

Biological self-organisation can be regarded as a process of spontaneous pattern formation; namely, the emergence of structures that distinguish themselves from their environment. This process can occur at nested spatial scales: from the microscopic (e.g., the emergence of cells) to the macroscopic (e.g. the emergence of organisms). In this paper, we pursue the idea that Markov blankets - that separate the internal states of a structure from external states - can self-assemble at successively higher levels of organisation. Using simulations, based on the principle of variational free energy minimisation, we show that hierarchical self-organisation emerges when the microscopic elements of an ensemble have prior (e.g., genetic) beliefs that they participate in a macroscopic Markov blanket: i.e., they can only influence - or be influenced by - a subset of other elements. Furthermore, the emergent structures look very much like those found in nature (e.g., cells or organelles), when influences are mediated by short range signalling. These simulations are offered as a proof of concept that hierarchical self-organisation of Markov blankets (into Markov blankets) can explain the self-evidencing, autopoietic behaviour of biological systems.

Dynamic phase transitions in the presence of quenched randomness

We present an extensive study of the effects of quenched disorder on the dynamic phase transitions of kinetic spin models in two dimensions. We undertake a numerical experiment performing Monte Carlo simulations of the square-lattice random-bond Ising and Blume-Capel models under a periodically oscillating magnetic field. For the case of the Blume-Capel model we analyze the universality principles of the dynamic disordered-induced continuous transition at the low-temperature regime of the phase diagram. A detailed finite-size scaling analysis indicates that both nonequilibrium phase transitions belong to the universality class of the corresponding equilibrium random Ising model.