New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈s〉=〈αs〉=0) and the correlated ordered (〈s〉 ≠0 and 〈α〉=〈s〉=0) states.     

Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation 〈S ₀ S _r 〉 decreases asymptotically asr ^?1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this “superfrustration” on the free energy and on the ground state properties is also discussed.     

Phase Diagram for Ashkin-Teller Model on Bethe Lattice

Using the recursion method, we study the phase transitions of the Ashkin-Teller model on the Bethe lattice, restricting ourselves to the case of ferromagnetic interactions. The isotropic Ashkin-Teller model and the anisotropic one are respectively investigated, and exact expressions for the free energy and the magnetization are obtained. It can be found that each of the three varieties of phase diagrams, for the anisotropic Ashkin-Teller model, consists of four phases, i.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Ferro, and two partially ordered ferromagnetic phases 〈σ〉and 〈σs〉, while the phase diagram, for the isotropic Ashkin-Teller model, contains three phases, i.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Baxter Phase, and the partially ordered ferromagnetic phase 〈σs〉.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on “pair propagation through a vertex”. The Bethe ansatz-type equations obtained reduce, in the case of lattice size N = 1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.     

The cross section of14N(n,p)14C at stellar energies and its role as a neutron poison forS-process nucleosynthesis

The absolute average cross section 〈σ〉 of the¹⁴N(n, p)¹⁴C reaction has been measured using neutron spectra that closely resemble Maxwell-Boltzmann distributions with thermal energies of kT=25.0 and 52.4 keV: 〈σ〉=0.81±0.05 and 0.52±0.06 mb, respectively. The resulting reaction rates are nearly the same at T₉=0.29 and 0.61, and their average, N_A〈συ〉=(1.3±0.1)×105 cm³ s^?1 mol^?1, is about a factor of three smaller than the previously adopted values obtained by extrapolation between thermal and higher-energy data. Thus, the¹⁴N(n, p)¹⁴C reaction plays a correspondingly smaller role as a neutron poison fors-process nucleosynthesis.     

A novel design of a photonic crystal sensor with improved sensitivity

Biosensors, based on photonic crystal (PC), are emergent subject. The use of PCs in this area brought solutions to both miniaturization and integration challenges that have been facing research groups for long time. We are only recently, by engineering such defects, able to propagate light in complex structures containing molecules of different sizes and shapes. We propose a novel structure containing defects with various sizes. The PC is formed by a dielectric cylinders with permittivity 8.9 (alumina Al₂O₃) and a radius r = 0.2a (a is the square lattice constant), arranged in a square lattice. We use the finite difference time domain to investigate the sensitivity of the proposed sensor to water. The defect based sensing element is introduced in two directions 〈0 1〉 and 〈1 0〉. These simulations show a better sensitivity to water than other analytes. It appears in the transmission curves where the peak shifts to high frequency when the refractive index is changed.     

Correlation inequality in Heisenberg ferromagnet

In a four-spin Heisenberg ferromagnetic system, it is found computationally that Griffiths' second inequality, ?〈σ_r·σ_s〉/?J_mn?0, m, n, r, s distinct, is violated, and conditions are obtained under which it holds.     

Scaling of heteroepitaxial island sizes

Monte Carlo simulations of an atomistic solid-on-solid model are used to study the effect of lattice misfit on the distribution of two-dimensional islands sizes as a function of coverage θ in the submonolayer aggregation regime of epitaxial growth. Misfit promotes the detachment of atoms from the perimeter of large pseudomorphic islands and thus favors their dissolution into smaller islands that relieve strain more efficiently. The number density of islands composed of s atoms exhibits scaling in the form N_s(θ) ~ θ/〈s〉²g(s/〈s〉) where 〈s〉 is the average island size. Unlike the case of homoepitaxy, a rate equation theory based on this observation leads to qualitatively different behavior than observed in the simulations.     

Green function theory of Curie and order—order transitions in ferromagnetic systems

Dipolar critical temperatures in ferromagnetic systems with isotropic bilinear and biquadratic exchange are investigated by means of the Green function technique. Expressions are found for both the familiar Curie temperature, T_c, and the less well known order-order transition temperature, T_o, at which, under appropriate conditions, the magnetic ordering undergoes a change between fully aligned and canted ferromagnetism. At T = 0, a fully aligned state has <s_i^z = s for spin s and all lattice sites i, while a canted state has 〈s_i^z〉<s. It is shown independently of the Green function analysis that the T = 0 ground state is fully aligned if α, the ratio of biquadratic to bilinear exchange integrals, obeys ?[2s(s?1)]^?1<α< [2s²?2s+1]^?1. The region below the lower limit is identified as the range in which canted ferromagnetism can occur and is a range that does not appear to have been considered previously via the Green function formalism.The temperature dependence of the magnetic ordering is investigated by means of the double-time temperature-dependent Green function formalism. A new decoupling scheme is derived and used to reduce higher order Green functions to lowest order. It is found that a canted state, occuring at low temperatures, undergoes a transition to a fully aligned state at a temperature T₀ and subsequently becomes disordered at temperature T_c. Transitions to paramagnetism are found to be second order for α<α_c and first order for α?α_c where α_c is a critical value that depends on the atomic spin and weakly on the lattice structure. A phase diagram is given to illustrate the results, and a comparison is made with the corresponding results found in mean field theory.     

Some AB-percolation problems in the antiferromagnetic potts model

The AB-correlated-site/random-bond percolation problem in a q-state antiferromagnetic Potts model on Bethe lattices is solved. We find the analytic expression of the AB-percolation characteristic functions in terms of the temperature, the external field and the active bond concentration p_B. The AB-threshold and the phase boundary of the system coincide at zero temperature and at most in two other points for every constant p_B > 1?σ. The properties of the Bethe lattice allow us to find the temperature dependent p_B which defines the AB-droplets, i.e. those special AB-clusters which diverge with thermal exponents along the phase boundary.     

Loose,Flat Knots in Collapsed Polymers

We consider single ring polymers which are confined on a plane but maintain a fixed three-dimensional knotted topology. The equilibrium statistics of such systems is studied on the basis of a model on square lattice in which the configurations are represented by N-step polygons with a number of self-intersections restricted to the minimum compatible with the topology. This allows to define the size, s, of the flat knots and to study their localization properties. Due to the presence of both excluded volume and attractive interactions, the model undergoes a theta transition. Accurate Monte Carlo results show that, while in the high temperature swollen regime both prime and composite knot components are localized (〈s〉 _N ～N ^t , with t=0), in the low temperature, compact phase they are fully delocalized (t=1). Right at the theta transition weak localization prevails (t=0.44±0.02). Part of the results can be interpreted by taking into account a dominance of figure eight shapes for the coarse grained knotted polymer configurations, and by applying the scaling theory of polymer networks of fixed topology. In particular t=3/7 can be conjectured as an exact exponent characterizing the weak knot localization at the theta point.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Stochastic flows,reaction — Diffusion processes,and morphogenesis

Recently, anexact procedure has been introduced [C. A. Walsh and J. J. Kozak,Phys. Rev. Lett. 47:1500 (1981)] for calculating the expected walk length 〈n〉 for a walker undergoing random displacements on a finite or infinite (periodic)d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of whichexact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processes in simple and multiple trap systems by reporting values of 〈n〉 for square (cubic) versus hexagonal lattices ind=2, 3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length 〈n〉 for the case of multiple walkers. Finally, we make contact with recent discussions of “mixing” by showing that the degree of chaos associated with flows in certain lattice systems can be calibrated by monitoring the lattice walks induced by the Poincaré map of a certain parabolic function.     

Model for the surface reconstruction phase transition of clean and hydrogen-adsorbed W(001) surfaces: Low-coverage solution

We summarize the theoretical indications and experimental evidence justifying a shortrange structural model for the clean and H-adsorbed W(001) surface reconstruction phase transition. A detailed study of the effect of the adsorbate treated as a lattice gas within the context of such a model is presented. The results, though based on mean field theory, are accurate in the low-cover-age region within the context of the model and succeed in reproducing the low-coverage features of the phase diagram, thus enabling a determination of some of the interaction constants in the model. The energy difference between distortions along the 〈11〉 and 〈10〉 directions is 3.0 × 10^?3 eV per atom. The force exerted on a surface W atom by an adsorbed H atom in an adjacent bridge site is $\text{0.04}\text{eV}\text{u}{}_0$, where u₀ is the magnitude of the clean surface W atom displacement at low temperature.     

Critical exponents for one-dimensional percolation clusters

For d=1, percolation clusters follow a scaling law with critical exponents σ=1 and τ=2. For the limit d→1, critical exponents can differ from their d=1 values, a complication which can already be studied in the simple Bethe lattice solution for cluster numbers.     

Pion structure functions from lattice QCD

We compute 〈x〉 and 〈x²〉 of the valence quarks in a pion, on the lattice using Wilson fermions in the quenced approximat We find 〈x〉 = 0.49±0.08 and 〈x²〉 = 0.02 at a scale μ ≅ 7 GeV, in a good agreement with experimental data.     

Dynamics of interaction of H2 and D2 with Ni(110) and Ni(110) surfaces

Elastic and direct-inelastic scattering as well as dissociative adsorption and associative desorption of H₂ and D₂ on Ni(110) and Ni(111) surfaces were studied by molecular beam techniques. Inelastic scattering at the molecular potential is dominated by phonon interactions. With Ni(110), dissociative adsorption occurs with nearly unity sticking probability s₀, irrespective of surface temperature T_s and mean kinetic energy normal to the surface 〈 E_⊥ 〉. The desorbing molecules exhibit a cos θ_e angular distribution indicating full thermal accommodation of their translation energy. With Ni(111), on the other hand, s₀ is only about 0.05 if both the gas and the surface are at room temperature. s₀ is again independent of T_s, but increases continuously with 〈 E⊥ 〉 up to a value of ～0.4 for 〈 E⊥ 〉 = 0.12 eV. The cos⁵θ_e angular distribution of desorbing molecules indicates that in this case they carry off excess translational energy. The results are qualitatively rationalized in terms of a two-dimensional potential diagram with an activation barrier in the entrance channel. While the height of this barrier seems to be negligible for Ni(110), it is about 0.1 eV for Ni(111) and can be overcome through high enough translational energy by direct collision. The results show no evidence for intermediate trapping in a molecular “precursor” state on the clean surfaces, but this effect may play a role at finite coverages.