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We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii?Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.

Considering in symmetrical half-length bond operations, we present in this paper two types of newly-developed generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively. Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.

The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics. The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various strengths of coupling between the two degrees of freedom is systematically calculated. The optimal diffusion path of the particle in a non-Ohmic damping system is revealed to have a probability to return to the potential valley under the combined influence of the off-diagonal system tensors., Comment: 10 pages, 5 figures

Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configurations reach the final state — ground state or frozen stripe state. For ground-state dynamical realization, the duration occurs when the energy per spin is 4/L, where L is the lattice size. For stripe-state dynamical realization, the energy is slightly higher than 2/L when the duration appears in the last evolution stage. In addition, it is found that the average energy per spin in final state is approximately 2/3L.

Two catalyzed-birth models of n-species (n≥2) aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Amk and Amj of the same species with the rate kernels Km(k,j) = Kmkj (m = 1,2,...,n, n≥2), and aggregates of An species catalyze a monomer-birth of Al species (l = 1,2,...,n−1) with the catalysis rate kernel Jl(k,j) = Jlkjυ. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution alk(t) of Al species depends crucially on the value of the catalysis rate parameter υ: (i) alk(t) obeys the conventional scaling law in the case of υ≤0, (ii) alk(t) satisfies a modified scaling form in the case of υ>0. In the second model, the mechanism of monomer-birth of An-species catalyzed by Al species is added on the basis of the first model, that is, the aggregates of Al and An species catalyze each other to cause monomer-birth. The kinetic behaviors of Al and An species are found to fall into two categories for the different υ: (i) growth obeying conventional scaling form with υ≤0, (ii) gelling at finite time with υ>0.

In this paper dynamical critical phenomena of the Gaussian model with long-range interactions decaying as on d-dimensional hypercubic lattices (d = 1, 2, and 3) are studied. First, the critical points are exactly calculated, and it is found that the critical points depend on the value of δ and the range of interactions. Then the critical dynamics is considered. We calculate the time evolutions of the local magnetizations and the spin-spin correlation functions, and further the dynamic critical exponents are obtained. For one-, two- and three-dimensional lattices, it is found that the dynamic critical exponents are all which agrees with the result when only considering nearest neighboring interactions, and that they are all δ if It shows that the dynamic critical exponents are independent of the spatial dimensionality but depend on the value of δ.

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and -dimensional Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality (or the fractal dimensionality ). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.

A new approach for exploring effects of interfaces on polar liquids is presented. Their impact on the polar liquid film motor (PLFM) – a novel micro-fluidic device – is studied. We account for the interface's impact by modeling slip boundary effects on the PLFM's electro-hydro-dynamical rotations. Our analytical results show as increases (with denoting the slip length resulting from the interface's impact on the film's properties, k > -1 and R denoting the film's radius): (a) PLFMs subsequently exhibit rotation characteristics under "negative-", "no-", "partial-" and "perfect-" slip boundary conditions; (b) The maximum value of the linear velocity of the steady rotating film increases linearly and its location approaches the film's border; (c) The decay of the angular velocities' dependency on the distance from the center of the film slows down, resulting in a macroscopic flow near the boundary. With our calculated rotation speed distributions consistent with the existing experimental ones, research aiming at fitting computed to measured distributions promises identifying the factors affecting , e.g., solid-fluid potential interactions and surface roughness. The consistency also is advantageous for optimizing PLFM's applications as micro-washers, centrifuges, mixers in the lab-on-a-chip.

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.

The decimation real-space renormalization group and spin-rescaling methods are applied to the study of phase transition of the Gaussian model on fractal lattices. It is found that the critical point equals /2 ( is the distribution constant of Gaussian model) on nonbranching Koch curves. For inhomogeneous fractal lattices, it is proposed that the is replaced with ( is the coordination number of the site ) and satisfies a certain relation . Under this supposition we find that the critical point of the Gaussian model on a branching Koch curve can be expressed uniquely as .

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-neighbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2 = −0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.