Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: partition function zeros approach

Magnetic ordering in strong anisotropic ferromagnetic bilayers with dipolar and antiferromagnetic interlayer exchange interactions: Monte Carlo approach

In this work, multilayer films consisting of two strong-anisotropic ferromagnetic layers antiferromagnetically coupled by a nonmagnetic spacer are studied by Monte Carlo simulations. The system is modeled by an Ising-based Hamiltonian that depends on both the intralayer exchange and dipolar constants and on the interlayer exchange constant (IEC). The ground state of the monolayers (null IEC) corresponds to alternate stripe domains with width h defined by the ratio between the exchange and dipolar constants (δ). The results show that IEC alters the energy balance that controls the stripe domain formation, leading to a ground state characterized by in-plane stripes out-plane antiferromagnetically coupled. When temperature increases two regimes are identified: an IEC-dominated regime where the orientational and positional orders are simultaneously lost in both layers, driving the system to the tetragonal liquid (TL) phase, and a dipolar-dominated one where signs of layers decoupling and the onset of positional disorder are observed. The last could be related with an intermediate nematic phase (NM). From the study of the nonequilibrium dynamics, the phase transitions to TL phase are characterized as continuous and those to the NM one as Kosterlitz-Thouless type. Also, for both layers the critical temperatures are the same and increase with IEC magnitude. Furthermore, the obtained critical exponents depend on the IEC values, which is indicative of a weak universality. For the dipolar-dominated regime, the decoupling between layers is also evidenced by the difference between their critical exponents.

Turing-like patterns in an asymmetric dynamic Ising model

To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in Ising models always relies on infinite-range interactions, this mapping allows us to design a finite-range-interactions Ising model that can produce patterns observed in reaction-diffusion systems including Turing patterns with a tunable typical length scale. This model has asymmetric interactions and several spin types coexisting at a site. While we use the example of genetic regulation during embryogenesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.

Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (h_{n}) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h_{n} to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h_{n}-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

Phase transitions and multicritical behavior in the Ising model with dipolar interactions

In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (h_{n}) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ. The obtained results indicate that the h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-TL line a weak first-order character is found in the interval 1.2585≤δ≤1.36 and becomes continuous for 1.37≤δ≤1.9. This result suggests the existence of a tricritical point close to δ=1.37. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.

Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: A short-time dynamics study

The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5≤δ≤1.3, where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5≤δ≤1.2 indicate that the phase transition line between the h=1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: a comparison for elastic flexible polymers

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from 13 to 309 monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.