Monte Carlo study of the antiferromagnetic two-dimensional Blume-Capel model

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

We develop a theory of charge storage in ultranarrow slitlike pores of nanostructured electrodes. Our analysis is based on the Blume-Capel model in an external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterizing the system, such as pore ionophilicity, interionic interaction energy, and voltage. The phase diagram includes the lines of first- and second-order, direct and re-entrant phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. Testing our predictions experimentally requires monodisperse, conducting ultranarrow slit pores, to permit only one layer of ions, and thick pore walls, to prevent interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and ionophobic pores and their underlying physics, may emerge in future experimental studies of more complex electrode structures.

Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement

The ion-ion interactions become exponentially screened for ions confined in ultranarrow metallic pores. To study the phase behaviour of an assembly of such ions, called a superionic liquid, we develop a statistical theory formulated on bipartite lattices, which allows an analytical solution within the Bethe-lattice approach. Our solution predicts the existence of ordered and disordered phases in which ions form a crystal-like structure and a homogeneous mixture, respectively. The transition between these two phases can potentially be first or second order, depending on the ion diameter, degree of confinement and pore ionophobicity. We supplement our analytical results by three-dimensional off-lattice Monte Carlo simulations of an ionic liquid in slit nanopores. The simulations predict formation of ionic clusters and ordered snake-like patterns, leading to characteristic close-standing peaks in the cation-cation and anion-anion radial distribution functions.

Magnetization plateaus in the antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.

Wetting transition in the two-dimensional Blume-Capel model: a Monte Carlo study

The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of L×M lattices where competing boundary fields ±H_{1} act on the first or last row of the L rows in the strip, respectively. We show that using the appropriate anisotropic version of finite-size scaling, critical wetting in d=2 is equivalent to a "bulk" critical phenomenon with exponents α=-1, β=0, and γ=3. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength H_{1c}(T) where critical wetting occurs goes to zero when the bulk second-order transition is approached, while H_{1c}(T) stays nonzero in the region where in the bulk a first-order transition from the ordered phase, with nonzero spontaneous magnetization, to the disordered phase occurs. Interfaces between coexisting phases then show interfacial enrichment of a layer of the disordered phase which exhibits in the second-order case a finite thickness only. A tentative discussion of the scaling behavior of the wetting phase diagram near the tricritical point is also given.

Monte Carlo study of the vector Blume-Emery-Griffiths model for 3He--4He mixtures in three dimensions

A version of the Vector Blume-Emery-Griffiths model with three-dimensional spins was studied on a simple cubic lattice by Monte Carlo simulations. We obtained the phase diagram, which reproduces, for a range of the parameters of the model, the topology of the one observed for bulk mixtures of 3He--4He. The phase diagram displays a superfluid, 4He-rich phase which undergoes a phase transition to a normal phase. This transition is first or second order, depending on the region of the phase diagram examined. One of the main features of this diagram is the existence of a tricritical point, which, for some values of the parameters of the model, decomposes into a critical endpoint and a double critical endpoint. These points were located with reasonable precision. This study provides the basis for the subsequent study of dynamic properties of 3He--4He mixtures.

Dynamic phase transition in the kinetic spin-1 Blume-Capel model under a time-dependent oscillating external field

We study within a mean-field approach the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Galuber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal field interaction D . We have obtained two types of solutions: a symmetric one, which corresponds paramagnetic phase where the magnetization (m) of the system oscillates in time around zero, and an antisymmetric one where m oscillates in time around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits one or more dynamic tricritical point, which depends on the values D . We also calculate the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

Universality and double critical end points

A double critical end point in the two-dimensional spin-3/2 Blume-Capel model is studied via extensive Monte Carlo simulations. The resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points.