Two-dimensional Ising model with alternate three-spin interactions in the horizontal direction and two-spin interactions in the vertical direction

A duality transformation is investigated for an Ising model in a rectangular lattice with alternate three-spin interactions in the horizontal direction and two-spin interactions in the vertical direction. The partition function is expressed by the one of the nearest-neighbour Ising model under an effective field in the rectangular lattice. It turns out that there is no phase transition in the system.     

Sierpinski镂垫上具有三体自旋作用的Gauss模型

应用实空间重整化群变换和累积展开相结合的方法，在Sierpinski镂垫上研究了二体自旋作用和三体自旋作用都存在时Gauss模型的相变和临界性质，求出了临界点和临界指数.与只有二体自旋作用的情况相比较，在无外场和有外场的情况下，临界点和临界指数都发生了变化，这表明三体自旋作用对其临界点和临界性质都有一定的影响. 关键词： Sierpinski镂垫 Gauss模型 重整化群 临界性质     

Two-spin correlation function of spin 12 Ising model on a bethe lattice

The two-spin correlation function of the Ising model on a Bethe lattice as a function of temperature and magnetic field. It is found that the coherence length is finite at finite temperatures.     

Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid

We study a two-dimensional ferrofluid of hard-core particles with internal degrees of freedom (plane rotators) and O(2)-invariant ferromagnetic spin interaction. By reducing the continuous system to an approximating reference lattice system, a lower bound for the two-spin correlation function is obtained. This bound, together with the Fröhlich–Spencer result about the Berezinskii–Kosterlitz–Thouless transition in the two-dimension lattice system of plane rotators, shows that our model also exhibits the same kind of ordering. Namely for a short-range ferromagnetic interaction the two-spin correlation function does not decay faster than some power of the inverse distance between particles, for small temperatures and high densities of the ferrofluid. For a long-range ferromagnetic interaction the model manifests a non-zero order parameter (magnetization) in this domain, whereas for high temperatures spin correlations decay exponentially.     

Spectral Gap and Exponential Decay of Correlations

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotation of a global symmetry of the system, we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself, rather than just the connected correlation function, decays exponentially under the gap assumption on a lattice with a certain self-similarity in (fractal) dimensions D < 2. In particular, if the system is translationally invariant in one of the spatial directions, then this self-similarity condition is automatically satisfied. We also treat systems with long-range, power-law decaying interactions.     

Magnetic-field-induced insulator-conductor transition in SU(2) quenched lattice gauge theory

We study the correlator of two vector currents in quenched SU(2) lattice gauge theory with a chirally invariant lattice Dirac operator with a constant external magnetic field. It is found that in the confinement phase the correlator of the components of the current parallel to the magnetic field decays much slower than in the absence of a magnetic field, while for other components the correlation length slightly decreases. We apply the maximal entropy method to extract the corresponding spectral function. In the limit of zero frequency this spectral function yields the electric conductivity of quenched theory. We find that in the confinement phase the external magnetic field induces nonzero electric conductivity along the direction of the field, transforming the system from an insulator into an anisotropic conductor. In the deconfinement phase the conductivity does not exhibit any sizable dependence on the magnetic field.     

Discrete Boltzmann equation for microfluidics

We propose a discrete Boltzmann model for microfluidics based on the Boltzmann equation with external forces using a single relaxation time collision model. Considering the electrostatic interactions in microfluidics systems, we introduce an equilibrium distribution function that differs from the Maxwell-Boltzmann distribution by an exponential factor to represent the action of an external force field. A statistical mechanical approach is applied to derive the equivalent external acceleration force exerting on the lattice particles based on a mean-field approximation, resulting from the electro-static potential energy and intermolecular potential energy between fluid-fluid and fluid-substrate interactions.     

Decay of correlations in Fermi systems at nonzero temperature

The locality of correlation functions is considered for Fermi systems at nonzero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at nonzero temperature.     

Electron spin decoherence in quantum dots due to interaction with nuclei

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei. The decay is caused by the spatial variation of the electron wave function within the dot, leading to a nonuniform hyperfine coupling A. We evaluate the spin correlation function and find that the decay is not exponential but rather power (inverse logarithm) lawlike. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by (planck)N/A, where N is the number of nuclei inside the dot, and the amplitude of precession decays to a finite value. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.     

The direct correlation function of a one-dimensional Ising model

The strictly finite range of the direct correlation function for a homogeneous nearest neughbor Ising chain is shown to persist in the presence of arbitrary site-dependent coupling constants and an arbitrary external field. A method is developed to examine the range of the direct correlation function for many-neighbor interactions. It is found from numerical examples that, in general, third-neighbor and higher interactions induce long-range direct correlations, as does the presence of a field in the second-neighbor case.     

A Feynman-Kac formula for the quantum Heisenberg ferromagnet. I

The Hamiltonian of the (anisotropic) quantum Heisenberg (anti-) ferromagnet on an arbitrary finite lattice is lifted to a Hamiltonian acting on sections of the bundle obtained by twisting a certain line bundle over the classical spin configuration space (which is a Kähler manifold) with the Dolbeault complex. This procedure is extended fromSU(2) to arbitrary compact semi-simple Lie groups and arbitrary irreducible representations. The Bott-Borel-Weil theorem gives a heat kernel representation for the original partition function in an external magnetic field. TheU(1)-gauged local Hamiltonian is the sum of the free, supersymmetric, twisted Dolbeault Laplace operator (multiplied by the inverse of an arbitrary small mass parameter) plus the lifted Hamiltonian.The resulting (Euclidean) Lagrangian is nonlocal and describes bosons which do and fermions which do not propagate through the lattice. All fields couple to the external magnetic field. The Lagrangian contains Yukawa and Luttinger type interactions.     

Magnetic properties of ferromagnetic diluted Zn x Cd1–x Cr2Se4 spinels are studied by Green's functions,mean field theory and high temperature series expansions theories

The field induced reorientation of the magnetization of ferromagnetic (or antiferromagnetic) structure is treated within the framework of many-body Green's function theory by considering all components of the magnetization. The mean field theory is used to calculate the nearest neighbour and the next-neighbour super-exchange J₁(Cr–Cr) and J₂(Cr–(Zn(Cd)–Se)–Cr), respectively, for the Zn_1–x Cd _x Cr₂Se₄ in the range 0 < x < 1. The intraplanar and the interplanar interactions are deduced. The high temperature series expansions (HTSEs) are derived for the magnetic susceptibility and the two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation (RPA). The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.     

Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

A one-dimensional quantum spin model with the competing two-spin and three-spin interactions is investigated in the context of a tensor network algorithm based on the infinite matrix product state representation. The algorithm is an adaptation of Vidal?s infinite time-evolving block decimation algorithm to a translation-invariant one-dimensional lattice spin system involving three-spin interactions. The ground-state fidelity per lattice site is computed, and its bifurcation is unveiled, for a few selected values of the coupling constants. We succeed in identifying critical points and deriving local order parameters to characterize different phases in the conventional Ginzburg-Landau-Wilson paradigm.     

Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain

We show that the spatial decay of plasmons in a periodic metal-nanoparticle chain is composed of exponential and power-law decays. Our results show a high level of similarity between the absorptive and radiative decay channels. By analyzing the poles (and the corresponding residues) of the generating function for the lattice Green's function, we explain the details of the spatial decay profile. We also present an analytical formula for the decay profile.     

Cross-relaxation in multiple pulse NQR spin-locking

The experimental and theoretical NQR multiple-pulse spin locking study of cross-relaxation process in solids containing nuclei of two different sorts I?>?1/2 and S?=?1/2 coupled by the dipole–dipole interactions and influenced by an external magnetic field. Two coupled equations for the inverse spin temperatures of the both spin systems describing the mutual spin lattice relaxation and the cross-relaxation were obtained using the method of the nonequilibrium state operator. It is shown that the relaxation process is realized with non-exponential time dependence describing by a sum of two exponents. The cross relaxation time is calculated as a function of the multiple-pulse field parameters which agree with the experimental data. The calculated magnetization cross relaxation time vs the strength of the applied magnetic field agrees well with the obtained experimental data.     

Chaotic walking and fractal scattering of atoms in a tilted optical lattice

We consider analytically and numerically chaotic walking of cold atoms in a tilted optical lattice created by two counter-propagating running waves with an additional external field in the semiclassical and Hamiltonian approximations. The effect consists in random-like changing the direction of atomic motion in a rigid lattice under the influence of a constant force due to a specific behavior of the atomic dipole-moment component that changes abruptly in a random-like manner while atoms cross standing-wave nodes. Chaotic walking generates a fractal-like scattering of atoms that manifests itself in a self-similar structure of the scattering function in the atom?Cfield detuning in the position and momentum spaces. We show that the probability distribution function of the scattering time decays in a non-exponential way with a power-law tail.     

Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.     

Dynamics of flux lines: thermal fluctuations

A relaxational dynamics for ad-dimensional model of flux lines is investigated. The flux lines are subject to thermal fluctuations such that they form a flux liquid rather than a flux lattice. We find that the density-density auto correlation function decays as (logt/t ²)² for large timest. In contrast, this correlation function decays for point-like vortices ast ^–2. At the transition to an empty lattice (Abrikosov-Meissner transition), the auto correlation function decays as a power law with dimension-dependent exponentsd+2 for flux lines andd for point-like vortices. Therefore, the fluctuations and the interactions of long flux lines have an accelerating effect on the relaxation.     

Ising lattice gauge theory in three dimensions

By raising the transfer matrix to a finite power the partition function for a finite lattice Z(2) gauge model is obtained exactly. The zeros of the resultant polynomial are found and some plaquette-plaquette expectation values are extracted. An exponential fit for the inverse correlation length matches onto both strong- and weak-coupling results but breaks down close to the second-order phase transition point.Similar calculations for the three-dimensional Ising model are also discussed.