Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s ⁴〉−3〈s ²〉²>0, i.e. in the region which we call Gaussian subjugation, where 〈s ^k 〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.     

Effect of the Dzyaloshinskii-Moriya interaction on heat conductivity in one-dimensional quantum Ising chains

The effect of the Dzyaloshinskii-Moriya (DM) interaction on the heat conduction in the quantum Ising chain has been studied by solving the Lindblad master equation. The chain is subject to a uniform transverse field h, while the exchange couplings {J _m } between the nearest-neighbor spins are either uniform, random or quasi-periodic. The average energy-density profile and the average energy current in the non-equilibrium steady state have been numerically calculated. The ballistic transport is observed in the uniform Ising chain with DM interaction. For the random Ising chain with DM interaction, the energy gradient is observed in the bulk of the spin chain whose energy current appears to scale as the system size ⟨Q⟩ ∼ exp(βN) with β < 0. For the quasi-periodic Ising chain with DM interaction, the J _m takes the two values J _A and J _B arranged in the Fibonacci sequence. The energy gradient also exists in the spin chain and the energy current behaves as ⟨Q⟩ ∼ N ^α with α < 0. By increasing the strength of the DM interaction D, a non-trivial transition from the thermal insulator heat transport to anomalous heat conduction is found in the Fibonacci Ising chain with large ratio of couplings λ = J _A /J _B . A rough phase diagram of λ vs. D is given in this paper as well.     

The Mixing Time Evolution of Glauber Dynamics for the Mean-Field Ising Model

We consider Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime (β < 1) has order n log n, whereas the mixing-time in the case β > 1 is exponential in n. Recently, Levin, Luczak and Peres proved that for any fixed β < 1 there is cutoff at time with a window of order n, whereas the mixing-time at the critical temperature β = 1 is Θ(n ^3/2). It is natural to ask how the mixing-time transitions from Θ(n log n) to Θ(n ^3/2) and finally to exp (Θ(n)). That is, how does the mixing-time behave when β = β(n) is allowed to tend to 1 as n → ∞. In this work, we obtain a complete characterization of the mixing-time of the dynamics as a function of the temperature, as it approaches its critical point β _c  = 1. In particular, we find a scaling window of order around the critical temperature. In the high temperature regime, β = 1 − δ for some 0 < δ < 1 so that δ ² n → ∞ with n, the mixing-time has order (n/δ) log(δ ² n), and exhibits cutoff with constant and window size n/δ. In the critical window, β = 1± δ, where δ ² n is O(1), there is no cutoff, and the mixing-time has order n ^3/2. At low temperature, β = 1 + δ for δ > 0 with δ ² n → ∞ and δ = o(1), there is no cutoff, and the mixing time has order . Research of J. Ding and Y. Peres was supported in part by NSF grant DMS-0605166.     

The singlet state in the Hubbard model with U=∞

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε ₀(n) of the N-state is lower than the energy ε _FM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than ε _FM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state. Zh. éksp. Teor. Fiz. 114, 2130–2144 (December 1998)     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Nuclear Spin Alignment and Alignment Correlation Terms in Mass A = 8 System

The pure nuclear spin alignments of ⁸Li and ⁸B were produced from the nuclear spin polarization applying the β-NMR method. The alignment correlation terms in the β-ray angular distribution were observed to test the G parity conservation in the nuclear β decay.     

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

The radial distribution function for a fluid in which the molecules interactvia a triangular well potential is considered. Expanding the radial distribution function in pwoers of βɛ, where ɛ is the depth of the potential andβ=1/k _BT the first-order terms are calculated analytically using the Percus-Yevick theory in the Baxter’s formulation. The first-order terms in the direct correlation functionc(r) are also calculated. The first- and second-order terms in the free energy obtained from the energy equation of state are calculated and compared with other calculations. An erratum to this article is available at .     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

Absorption spectrum and excitons in thin films of the solid electrolyte RbCu4Cl3I2

We have investigated the absorption spectrum of thin films of the superionic conductor RbCu₄Cl₃I₂ synthesized on NaCl crystalline substrates. It is shown that the electron and exciton excitations in the energy interval 3–6 eV are associated with optical transitions in the CuHal sublattice, and the edge of the fundamental band is controlled by optical transitions in the Cu(II)Hal sublattice. It is found that the large band gap of this compound (E _g =3.86 eV) in comparison with those of CuCl and CuI is a result of the small number of Cu ions in the second coordination sphere. The temperature dependence of the spectral position and half-width of the low-temperature exciton band reveals features associated with the phase transitions γ→β (T _c1=170 K) and β→α (T _c2=220 K) and with disordering of the cation sublattice attendant to the transition to the superionic state. Fiz. Tverd. Tela (St. Petersburg) 40, 1022–1026 (June 1998)     

On the limit of nuclear stability — The region of double magic100Sn and bound-state β-decay of187Re75+

Experiments which led to the discovery of the heaviest, self-conjugated double magic nucleus¹⁰⁰Sn and the bound-state β-decay of completely ionized¹⁸⁷Re are presented.¹⁰⁰Sn was produced by fragmentation of 1.1 A GeV¹²⁴Xe beams, separated and implanted in a 4π Si-stack detector. From its decay a half-lifeT _1/2=0.94(+0.54, −0.27) s and a β⁺ endpoint energy ofE _β=3.4(+0.7, −0.3) MeV were determined for the 0⁺−1⁺ Gamov-Teller transition. Completely stripped¹⁸⁷Re⁷⁵⁺ was produced and stored in a coolerring with an energy of 351 A MeV for several hours. The products of bound-state β-decay of¹⁸⁷Re⁷⁵⁺ were detected by two independent methods, which allowed to determine a half-life ofT _1/2=33±6 y for this decay, which is of importance for the calibration of the Re/Os nucleosynthesis chronometer.     

Thermodynamic parameters of diffuse phase transitions in Ag2Te

A differential thermal analysis in vacuum and studies of the coefficients of electrical conductivity and thermal conductivity, and of the thermal emf are made in Ag₂Te in the neighborhood of the structural phase transition. It is shown that these data can be used to calculate the switching factor L(T), determine the region in which the phases coexist within the transition, and calculate the thermodynamic parameters. Prior to and after the main phase transition, additional displacement transitions are observed. It is found that the phase transition takes place roughly according to the scheme α _{385 K}→α′_{405 K}→β′_{420 K}→β _{440 K}. The specific heat C _p, changes in entropy ΔS and transition enthalpy ΔH, as well as the minimum phase fluctuation volume V, and the heat Q of the phase transition are determined. It is shown that excesses of Te and Ag have almost no effect on the transition temperatures T ₀, but have a substantial effect on the thermodynamic parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1693–1697 (September 1998)     

A Generalized Plasma and Interpolation Between Classical Random Matrix Ensembles

The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings β=1,2 and 4. It has been known for some time that there is an exactly solvable two-component log-potential plasma which interpolates between the β=1 and 4 circular ensemble, and an exactly solvable two-component generalized plasma which interpolates between β=2 and 4 circular ensemble. We extend known exact results relating to the latter—for the free energy and one and two-point correlations—by giving the general (k ₁+k ₂)-point correlation function in a Pfaffian form. Crucial to our working is an identity which expresses the Vandermonde determinant in terms of a Pfaffian. The exact evaluation of the general correlation is used to exhibit a perfect screening sum rule.     

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r×r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case r = 1, this reproduces well-known results of Wilson and others from the 1990’s relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators.      

CsCl effect on the optical properties of the 80GeS2–20Ga2S3 base glass

Optical properties of chalcogenide glasses belonging to the series (80GeS₂–20Ga₂S₃)_100−x (CsCl) _x with x=0;5;10;15;20 were investigated. The linear refractive indices (n ₀) were determined by prism measurements at four wavelengths: 633 nm, 825 nm, 1311 nm, and 1511 nm. Z-scan experiments were performed at 800 nm to measure the non-linear indices (n ₂) and the absorption coefficients (β). CsCl additions in the base glass (80GeS₂–20Ga₂S₃) are characterized by a white shift of the transmission in the visible range and a strong decrease of both n ₀ and n ₂. As the same time, β is also decreasing and this results in a figure of merit FOM=2βλ/n ₂ that remains relatively low at 800 nm, meaning that this series of highly non-linear glasses should be very suitable for optical switching applications at telecommunication wavelengths.     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

Experimental study of the <Emphasis Type="Italic">πh</Emphasis><Subscript>11/2</Subscript> band in <Superscript>113</Superscript>Sb

In the present work, the excited states of ¹¹³Sb were populated in the ¹⁰⁰Mo(²⁰Ne, p6n) reaction at a beam energy of 136 MeV. States only up to 59/2⁻ were observed in the ΔJ = 2 band. Mean lifetimes for the five states (from 4460 to 7998 keV) were measured for the first time using Doppler shift attenuation method. An upper limit of the lifetime (0.14 ps) was estimated for the 9061 keV, 47/2⁻ state. The B(E2) values, derived from the present lifetime results, correspond to a large quadrupole deformation of β ₂ = 0.32. The observed reduction in the experimental B(E2) values for the 918.4 keV (spin 39/2⁻ → 35/2⁻) and 985 keV (spin 43/2⁻ → 39/2⁻) transitions may be interpreted as due to the proton alignement in the g _7/2 orbital. The dynamic moment of inertia was observed to be about half of the rigid body value at the highest observed frequency.     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure (p = 1.00) and weakly diluted (p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.     

Scaling function near a transition to an insulator state

Analysis of experimental results yields a scaling function of the form β(g)=121/g near the metal-insulator transition in three-dimensional systems. In two-dimensional electronic systems demonstrating a transition to an insulator state, the same relation holds for the function νβ, where ν is the critical exponent characterizing the divergence of the correlation length. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 807–811 (10 December 1998)     

Phase transitions in the framework of complete version of IMB-1

The classical energy functional of complete IBM-1 model version is studied in terms of nuclear shape variables (β, γ), employing two essential control parameters (r ₂, r ₁) used in catastrophe theory formalism. The dependence of energy surface equilibrium values from deformation parameter β is analyzed in the case when γ = 0. The results, obtained for critical points and phase transition lines between spherical (β = 0) and two deformed (β > 0, β < 0) shapes, are compared with the ones, following from the studies, in which the simplified extended Casten triangle version of interacting boson model was used. Original Russian Text ? J. Proskurins, A. Andrejevs, T. Krasta, J. Tambergs, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 241–244. The article is published in the original.