Boundary conformal field theory approach to the critical two-dimensional Ising model with a defect line

We study the critical two-dimensional Ising model with a defect line (altered bond strength along a line) in the continuum limit. By folding the system at the defect line, the problem is mapped to a special case of the critical Ashkin-Teller model, the continuum limit of which is the Z₂ orbifold of the free boson, with a boundary. Possible boundary states on the Z₂ orbifold theory are explored, and a special case is applied to the Ising defect problem. We find the complete spectrum of boundary operators, exact two-point correlation functions and the universal term in the free energy of the defect line for arbitrary strength of the defect. We also find a new universality class of defect lines. It is conjectured that we have found all the possible universality classes of defect lines in the Ising model. Relative stabilities among the defect universality classes are discussed.     

一种具有次近邻相互作用的Transverse XY模型

本文推广Transverse XY模型量子链至次近邻相互作用情况,考虑哈密顿量 H=g∑_nσ_n²-∑_n ((1+γ)/2σ_n^xσ_n+1^x+(1-γ)/2σ_n^yσ_n+1^y)-λ∑_n ((1+β)/2σ_n^xσ_n+2^x+(1-β)/2σ_n^yσ_n+2^y)。当β=0以及γ≠0时,证明在临界点附近它对应于一自由费密场,从而属伊辛普适类。 关键词：     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics

Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T _x ?and?T _y , and also different time-scale constants, ?? _x and ?? _y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.     

Majority-vote model with different agents

We consider the majority-vote model with noise in a network of social interactions for a system with two classes of individuals, class σ and class τ. For the two-agent model each class has its own dynamics, with individuals of σ class being influenced by neighbors of both classes, while the individuals of type τ are influenced only by neighbors of that class. We use Monte Carlo simulations and finite-size scaling techniques to estimate the critical properties of the system in the stationary state. The calculated values of the critical noise parameters, and , allow us to identify five distinct regions in the phase diagram on the q_τ-q_σ plane. The critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two-dimensional Ising model.     

Critical exponents of Z2 gauge theory in (3 + 1) dimensions

We calculate the critical coupling and the critical exponents for the deconfinement transition of Z₂ gauge theory, using Monte Carlo simulation with finite-size scaling techniques. Our results agree well with the universality predictions based on the 3-dimensional Ising model.     

The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc

The form-factor bootstrap approach is used to compute the exact contributions in the large-distance expansion of the correlation function 〈σ(x)σ(0)〉 of the two-dimensional Ising modeliin a magnetic field at T = T_c The matrix elements of the magnetization operator σ,(x) present a rich analytic structure induced by the (multi-)) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.     

Cubic harmonic analysis of magnetic anisotropy measurements on single crystal HoxTb1−xFe2 laves phase compounds

Room temperature magnetic anisotropy measurements have been made on a series of low anisotropy Ho_xTb_1?xFe₂ compounds, with 0.826 < x < 0.908, using torque magnetometry techniques. An analysis of the data using the conventional expansion of anisotropy energy in terms of the direction cosines proved inadequate because of the presence of higher order contributions to the anisotropy. When these contributions were included in the expansion, non unique anisotropy constants were obtained which were not consistent with the predictions of the single ion model. An analysis of the data using an expansion of the anisotropy in terms of an orthonormal set of functions, namely the cubic harmonics developed by Mueller and Priestly, proved more successful. The results showed that the two lowest order anisotropy constants, κ₄ and κ₆, both varied linearly with holmium concentrations as predicted by the single ion model; however, κ₈, the next higher order term, was not consistent with the predicted behavior. The origin of this contribution is believed to be related to the magnetostriction.     

Representations and inequalities for Ising model Ursell functions

We describe and investigate representations for the Ursell functionu _n of a family ofn random variables {σ _i}. The representations involve independent but identically distributed copies of the family. We apply one of these representations in the case that the random variables are spins of a finite ferromagnetic Ising model with quadratic Hamiltonian to show that (?1) ^n/2+1 u _n(σ ₁, ...,σ _n) ≧ 0 forn=2, 4, and 6 by proving the stronger statement \(( - 1 )^{\frac{n}{2} + 1} \frac{{\partial ^m }}{{\partial J_{i1j1} \cdots \partial J_{imjm} }}Z^{\frac{n}{2}} u_n \left| {_{J = 0} } \right. \geqq {}^\backprime 0\) forn=2, 4, and 6, theJ _ij being coupling constants in the Hamiltonian andZ the partition function. For generaln we combine this result with various reductions to show that sufficiently simple derivatives of (?1) ^n/2+1 Z ^n/2u_n, evaluated at zero coupling, are nonnegative. In particular, we conclude that (?1) ^n/2+1 u _n ≧ 0 if all couplings are nonzero and the inverse temperature β is sufficiently small or sufficiently large, though this result is not uniform in the ordern or the system size. In an appendix we give a simple proof of recent inequalities which boundn-spin expectations by sums of products of simpler expectations.     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

Elastic stress fields caused by a dislocation in Ge x Si1−x /Si film-substrate system

The elastic stress fields caused by a dislocation in Ge_xSi_(1-x) epitaxial layer on Si substrate are investigated in this work. Based on the previous results in an anisotropic bimaterial system,the image method is further developed to determine the stress field of a dislocation in the film-substrate system under coupled condition. The film-substrate system is firstly transformed into a bimaterial system by distributing image dislocation densities on the position of the free surface. Then,the unknown image dislocation densities are solved by using boundary conditions,i.e.,traction free conditions on the free surface. Numerical simulation focuses on the Ge0.1Si0.9/Si film-substrate system. The effects of layer thickness,position of the dislocation and crystallographic orientation on the stress fields are discussed. Results reveal that both the stresses σxx,σxz at the free surface and the stress σxy,σyy,σyz on the interface are influenced by the layer thickness,but the former is stronger. In contrast to the weak dependence of stress field on the crystallographic orientation the stress field was strongly affected by dislocation position. The stress fields both in the film-substrate system and bimaterial system are plotted.     

Is the peak value of σ xx at the quantum Hall transition universal?

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σ _xx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σ _xx is reduced by a factor (1 + g/2π)^?1, at least for small g. This provides some theoretical evidence for the non-universality of σ _xx , as observed in a number of experiments.     

Yukawa alignment in a multi Higgs doublet model: An effective approach

In the two Higgs doublet model, natural flavour conservation can be achieved through the use of a discrete Z₂$Z_2$ symmetry. A less restrictive condition is the requirement of alignment in the Yukawa sector. So far, alignment has been an ansatz, not rooted in a specific model. In this Letter we present a model for alignment, which starts with 2+N$2+N$ Higgs doublets, with natural flavour conservation imposed by a discrete symmetry. Only two of these scalars couple to the fermions, the other N scalars are in a hidden sector. Assuming that the two scalar doublets coupled to fermions are heavy, their decoupling leads to an effective Yukawa interaction. The latter connects the fermions and the scalars of the hidden sector, and exhibits the same Yukawa coupling matrix for each of the N scalars.     

Nearest neighbor ising model with added local 4-spin interaction

The effects of adding a local 4-spin term to the nearest neighbor Ising model are studied. The relevant parameter isx, the ratio of the four- to the two-spin interaction strength. We have evaluated the first six terms of the high temperature susceptibility expansion and found them to be consistent with the value 1.75 of the critical exponent γ. The critical exponent α is shown to remain zero to first order inx, provided that the free energy is analytic inx. We also demonstrate the equivalence of the model examined to an elastic spin system with pure two-spin interactions.     

Liouville field theory coupled to a critical Ising model: non-perturbative analysis,duality and applications

Two different kinds of interactions between a $\text{Z}{}_{\mathrm{n}}$-parafermionic and a Liouville field theory are considered. For generic values of n, the effective central charges describing the UV behavior of both models are calculated in the Neveu–Schwarz sector. For n=2 exact vacuum expectation values of primary fields of the Liouville field theory, as well as the first descendent fields are proposed. For n=1, known results for sinh-Gordon and Bullough–Dodd models are recovered whereas for n=2, exact results for these two integrable coupled Ising–Liouville models are shown to exchange under a weak–strong coupling duality relation. In particular, exact relations between the parameters in the actions and the mass of the particles are obtained. At specific imaginary values of the coupling and n=2, we use previous results to obtain exact information about: (a) integrable coupled models like Ising–$\text{M}{}_{\mathrm{p/p\prime }}$, homogeneous sine-Gordon model SU(3)₂ or the Ising–XY model, (b) Neveu–Schwarz sector of the Φ₁₃ integrable perturbation of N=1 supersymmetric minimal models. Several non-perturbative checks are done, which support the exact results.     

Scaling law for the fluid-solid phase transition in Yukawa systems (dusty plasmas)

Yukawa systems serve as models for plasmas and colloidal suspensions of charged particles. The state of these systems is determined by two dimensionless parameters: k = a/λ _D , which is the ratio of the mean interparticle distance to the Debye length λ _D , and Γ = Z _d ² e ²/aT _d , which is the ratio of the Coulomb potential energy to the particle temperature T _d (Z _d is the charge of each particle). We propose an empirical scaling law for the critical coupling parameter Γ _c needed for crystallization in Yukawa systems. The dependence of Γ _c on k is in good agreement with recent molecular dynamics simulations.     

Dynamic magnetic properties in the kinetic mixed spin-2 and spin-5/2 Ising model under a time-dependent magnetic field

We extend the recent paper [W. Jiang, V-C. Lo, B-D. Bai, J. Yang, Physica A 389 (2010) 2227-2233] to present a study, within a mean-field approach, the dynamic magnetic properties of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system, which corresponds the molecular-based magnetic materials AFe^IIFe^III(C₂O₄)₃ [ A=N(n-C_nH_2n+1)₄, n=3-5], by using the Glauber-type stochastic dynamics. This mixed Ising ferrimagnetic system is used on a layered honeycomb lattice in which Fe^II (S=5/2) and Fe^III (σ=2) occupy sites. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first-or second-order) phase transitions. We also present the dynamic phase diagrams and study the dynamic magnetic hysteresis loop behaviors of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system. The results are compared with some experimental and theoretical works and a good overall agreement is found.     

Electrical conductivity of nonstoichiometric Ba β-alumina single crystals prepared by a floating zone method

Nonstoichiometric Ba β-alumina single crystals, Ba_1−0.25xMg_1−xAl_10+xO_17+0.25x (0≦x≦1), were prepared in the BaO–MgO–Al₂O₃ system by a floating zone method. The single crystals were cleaved parallel to a (001) plane. The electrical conductivity parallel to the cleavage plane (σ_//) was 10 to 20 times greater than that perpendicular to the cleavage plane (σ_⊥). The σ_// and σ_⊥ had the maximum at around x=0.5. The activation energy of σ_⊥, 240 to 270 kJ/mol, was slightly greater than that of σ_//, 170 to 190 kJ/mol. The σ_// was almost independent of oxygen partial pressure (P_O2), while σ_⊥ showed a P_O2^−1/6 dependence in a low P_O2 region of P_O2=10⁻⁴ to 10⁻¹³ Pa.     

Systematic study of impact parameter dependent K-vacancy probabilities in near symmetric gas- and solid-target collision systems

K-vacancy production probabilitiesP _K (b) were measured with gas and solid targets byK-x-ray particle coincidences (impact parameterb is determined by the particle detection angle) in the region of light (Z _P ?Z _T ?10) up to intermediate heavy (Z _P ?Z _T ?36) collision systems. The measuredP _K (b) reveal a very strong difference in shape between solid and gas targets independent ofZ. Only theP _K (b) measured with gas targets and those measured with solid targets at very small impact parameters show reasonable good agreement with the 2pπ _x-2pσ rotational coupling model. At largeb theP _K (b) from solid targets are strongly influenced by a multiple collision effect, where projectileL-vacancies seem to be produced in collisions beforeK-vacancy production. However, this effect cannot be understood just by a two collision process whereL-vacancy production and 2pπ _x-2pσ rotational coupling occurs in consecutive collisions.