Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions (original) (raw)
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Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
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 ...
Influence of the Pair Correlations on the Phase Transition in an Ising Lattice
Physical Review
We propose a method to incorporate pair correlations of an Ising lattice system in molecular field theory to higher orders. The theory is applied to ferromagnetism, where a system of equations is obtained for the response function (here the susceptibility). We obtain important corrections on the Weiss model and the spherical model. This is illustrated by an explicit calculation of the critical temperature and the spurious phase, appearing for T > T., near the critical point in the case of a simple cubic lattice.
Phase Transition in 2D Ising Model with Next-Neighbor Interaction
Journal of physics, 2019
We used a Monte Carlo method to analyze a planar Ising model taking into account a ferromagnetic interaction with next neighbors. We found that independent of the value of the additional interaction, the character of singularity of the heat capacity did not change. Namely, at the critical point the heat capacity has a logarithmic singularity. We obtained a semitheoretical formula relating the value of the critical temperature with the value of the additional ferromagnetic interaction.
Phase transitions in the frustrated Ising model on the square lattice
Physical Review B, 2013
We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 < 0 (nearest neighbor, ferromagnetic) and J2 > 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g = J2/|J1| > 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 < g < g * , where g * = 0.67 ± 0.01. Thereafter, the transitions from g = g * to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well known Ashkin-Teller model from its 4-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g * in the J1-J2 model. The continuous transitions near g * can therefore be mistaken to be first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g > 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.
Physical Review E, 2012
We have performed multicanonical simulations to study the critical behavior of the twodimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction δ where the phase characterized by striped configurations of width h = 1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between δ = 0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents ν that are clearly consistent with a single second-order phase transition line, thus excluding such tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.
Phase transitions and multicritical behavior in the Ising model with dipolar interactions
Physical review. E, 2016
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 ...
Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions
Physical Review E, 2019
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 lowtemperature 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.
Metastable states in a two-dimensional Ising model with dipolar interactions
Physica D: Nonlinear Phenomena, 2002
The equilibrium phase diagram of a two-dimensional Ising model with competing exchange and dipolar interactions is analyzed using a Monte Carlo simulation technique. We consider the low temperature region of the (δ, T ) phase diagram (δ being the ratio between the strengths of the exchange and dipolar interactions) for the range of values of δ where striped phases with widths h = 1 and 2 are present. We show that the transition line between both phases is a first order one. We also show that, associated with the first-order phase transition, there appear metastable states of the phase h = 2 in the region where the phase h = 1 is the thermodynamically stable one and vice versa.
Monte-Carlo simulation of phase transition in 2D and 3D ising model
Scientific World
In this work, Markov Chain-Monte Carlo technique was used to study the phase transition in two and three dimensional Ising Model (IM) in a square and cubic lattice. The study of temperature dependence of average magnetization and specific heat in different magnetic fields has been carried out in the 3x3 and 3x3x3 lattice with periodic boundary. Critical temperature point kBTc / J for 2D and 3D Ising Model has been observed at around 2.2 and 4.3 respectively at zero field. Our work satisfies Onsager’s critical value in 2D IM. The simulation suggests bifurcation in average magnetization below critical temperature Tc. Temperature plays the role of increasing randomness of spins. We found that Ising Model in small lattice size still retains interesting features like spontaneous magnetization and symmetry breaking below Tc at B = 0. At a non-zero field, the likelihood of spins to prefer certain alignment depends on the direction of the external field and magnitude of magnetization depend...
Analysis of the phase transition for the Ising model on the frustrated square lattice
Physical Review B, 2011
We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearestand strong next-nearest neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2 < J2/J1 1 is not of the weakly universal type-as commonly believed-but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1 = 0), we calculate the effect of the nearest neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.