Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

Low temperature thermal expansion and magnetostriction of TmCd

Thermal expansion measurements in various external magnetic fields confirm the recently found Jahn-Teller transition in TmCd at 3.16 K. The tetragonal strain ?₃ at T = 0 K is found to be 0.62 × 10^?3. From magnetostriction data we determine a coupling constant g₀² = 0.4 × 10^?3 K which is in good agreement with the value found from ultrasonic experiments. In order to explain our magnetostriction results in the cubic phase, g₀ has to be taken negative.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L ^d–1 × L _z , characterizing by parameters L/ξ and L _z /L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ? obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.     

Specific heat of NaNO2 near its transition points

Using an a.c. technique, the specific heat of NaNO₂ was measured as a function of temperature near its antiferroelectric-to-paraelectric phase transition point (T_N). The transition was found to be of the second order. The critical exponents are; α = 0·38 for ? = 2 × 10^?4 ～ 1 × 10^?1, and α′ = 0·18 for ? = ?2 × 10^?4 ～ ?3 × 10^?3. The critical exponents deduced from the scaling-law relations are roughly close to the values obtained from a random phase approximation for a system with an isotropic interaction. However, a difference was recognized between the observed exponent for the specific heat and the values theoretically given for T > T_N by the random phase approximation for a system with a short-range interaction or for a system with a long-range dipolar interaction. A thermodynamical analysis was made by using the generalized Pippard relation, and the present result was found to be consistent with the pressure dependence of the antiferroelectric transition point.     

Phase transitions in adsorbed films of barium on W(011)

Phase transitions in barium submonolayers adsorbed on W(011) are studied in a wide range of temperatures and coverages by the LEED technique, including the temperature measurement of the diffraction intensity. The regions of ordered and disordered structures are determined, the result is presented in the form of phase diagram. The temperature dependence of the adfilm Bragg intensity in the low temperature limit (the lowest temperature is 5 K) shows an appreciable slope for all incoherent and almost all coherent structures, except for (3×2). The fact is discussed in terms of the adfilm long- and quasi-long-range order. The disordering of the (3 × 2) lattice near T_c=130 K is the second-order phase transition with the order parameter critical exponent β=0.16. the adfilm is two-phase in the range n=(3.2?3.8)×10¹⁴cm^?2 and singlehase for the rest of the coverages. The effect of the first-order phase transition on the character of the work function change in the two-phase region is discussed.     

n+1维双sine-Gordon模型的Coleman相变

本文计算了n+1维双sinc-Gordon模型的高斯有效势,在高斯有效势近似下,证明:n≥3的模型是平凡的,n<3的模型存在一个Coleman相交点,临界耦合参数为β_cr=(2ⁿ⁺²π^(n+1)/2(α_1R+α_2R/4)^(3-n)/2)/(Γ(1/2(3-n))(α_1R+α_2R/16)). 关键词：     

Hadron mass calculations with Susskind and Wilson fermions in the fundamental-adjoint plane

We report the results of hadron mass calculations in the valence (quenched) approximation, on an 8³ × 16 lattice. For Wilson fermions with the standard Wilson action we find good agreement with results form the hopping parameter expansion on a 16⁴ lattice at β = 5.7, with only a small finite size effect in the anticipated direction. The proton-to-rho mass ration is however too high by 60% and the delta-proton mass difference is too small. We have repeated these calculations at two points of the same string tension in the plane of the fundamental and adjoint couplings, in an attempt to avoid the unphysical critical point there; within statistical errors the meson masses remain the same, there is an improvement in the delta-proton splitting and the proton mass decreases slightly, but not enough to produce agreement with experiment. The estimates of lines of constant string tension obtained as a preliminary to the mass calculation are in good agreement with weak coupling expansions at the larger β values and cross over towards strong coupling predictions around β = 5.7. Also, crude estimates reveal the disappearance of the specific heat peak as one moves away from the unphysical singularity. For Susskind fermions we find some measure of agreement with other results form a 10³ × 16 lattice, but large, apparently finite size, effects in the rho mass at low quark mass. Meson masses in lattice units disagree with the Wilson fermion results by as much as a factor of 2. This disagreement persists in the fundamental-adjoint plane, suggesting the importance of studying improved fermion actions. At β = 6.0, Wilson fermion results show clear finite size effects on the 8³ × 16 lattice.     

The calculation of critical amplitudes in SU(2) lattice gauge theory

We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3 + 1)-dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling functions. As a guiding line for determining the critical amplitudes we use envelope equations which we derive from the finite size scaling formulae of the observables. We have produced new high precision data on N_{σ³ × 4} lattices for N_χ = 12, 18, 26 and 36. With these data we find different corrections to the asymptotic scaling behaviour above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C₊/C₋ = 4.72(11) and thus in excellent agreement with a recent measurement for the 3d Ising model.     

Central peak for a scalar ϕ 4-model: mode coupling approach revisited

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T _c. For a scalar ? ⁴-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T _c'(≥ T _c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ? ⁴- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T ₀'obtained from the Ginzburg criterion sets an upper bound for T _c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.     

Detection of deep centers in semiconductors by strain modulated electron spin resonance: Pt+ in si

Strain-modulated ESR of p⁺-type silicon, doped with Pt (1.4 × 10¹⁷ Pt cm^-3) reveals a spectrum, characteristic of a triplet state. It is tentatively attributed to Pt⁺?Pt⁺ pairs. The g-factor (g = 1.94±0.01) is isotropic and extremely sensitive to strain: if we write δg = Fε we find ∥F∥? 2×10⁴ as an order of magnitude estimate. The exchange coupling is ferromagnetic and predominantly isotropic.     

Neutron study of a displacive phase transition in N-nitrodimethylamine (DMN): High and low frequency vibrational modes; high pressure effect on the transition temperature; principal compressibilities

N-Nitrodimethylamine is known to undergo a displacive structural phase transition at T_t～107 K, (atmospheric pressure) associated with a soft-mode observed in the low temperature phase Raman spectrum.The soft-model has already been assigned to a lattice vibration although crystallographic observations of the symmetry breaking distortion suggest that a coupling with an internal vibration should not be ruled out. To clarify this point neutron inelastic spectra have been recorded. They lead to a better assignment of both the high and low frequency vibrations and to the conclusion that no softening of an intramolecular mode is visible.High pressure (up to 3.5 Kbars) neutron scattering experiments are also described. They give both the directions and magnitudes (k₁=0.33× 10^?2, k_b=1.17 × 10^?2, k₃ = 0.12× 10^?2Kbar^?1) of the isothermal principal compressibilities of DMN and the dependence of T_t on pressure ((dT_t/dP)_P=0 ～ + 4.3 Kbar^?1). Spectroscopic and crystallographic data now available on DMN allow us to discuss the mechanism of the transition. An extension of Samara's rule to molecular crystals is attempted     

Monte carlo study of anSU(2) lattice gauge-Higgs theory at finite temperature

AnSU(2) gauge theory coupled to a Higgs field in the fundamental representation is studied at finite temperature by Monte Carlo method. Calculations are done on 8⁴, 8³×4 and 8³×2 lattices with a small Higgs self-coupling constant. In the parameter region we studied both the location and the order of the Higgs transition are found to be insensitive to the system's temperature. As for the deconfining transition at finite temperature, our data suggest that it disappears within the symmetric region as the Higgs bare mass decreases. Results on the Higgs energy density and the gauge energy density are also presented.     

Connected Green function approach to symmetry breaking inΦ 1+1 4 -theory

Using the cluster expansions for n-point Green functions we derive a closed set of dynamical equations of motion for connected equal-time Green functions by neglecting all connected functions higher than 4 ^th order for theλΦ ⁴-theory in 1 + 1 dimensions. We apply the equations to the investigation of spontaneous symmetry breaking, i.e. to the evaluation of the effective potential at temperatureT=0. Within our momentum space discretization we obtain a second order phase transition (in agreement with the Simon-Griffith theorem) and a critical coupling ofλ _crit /4m ²=2.446 as compared to a first order phase transition andλ _crit /4m ²=2.568 from the Gaussian effective potential approach.     

Evidence for the two-body nature of theE1 transition operator in the sdf-interacting boson model

Two new absolute transition rates are reported for the nucleus¹⁴⁴Sm following an (α, α′) Coulomb excitation study. They are B(E3; 3^?→ 0⁺)=(38±3) W.u. and B(E1;3^? → 2⁺)=(2.8±0.4)×10^?3 W.u. This large E1 matrix element, along with the previously known B(E1; 1^? →⁺) value support the interpretation of the 1^? state in this nucleus as 2-phonon 2⁺ × 3^? excitation. In the frame of the IBM-1 +f-boson model we show the need for a two-body term in the E1 transition operator. Estimates for the strengths of the one and two-body parts of the E1 transition operator are obtained from these experimental data.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

Measurement of the ortho-para transition rate in the pμp molecule and deduction of the pseudoscalar coupling constant gpμ

The ortho-para transition rate in the pμp molecule has been found experimentally to be λ_OP = (4.1 ± 1.4) × 10⁴ s^?1. Our recent result for the muon capture rate in liquid hydrogen can now be interpreted to extract the ortho-molecular capture rate: λ_OM = (531 ± 33) s^?1. A deduction of the pseudoscalar coupling constant g_p^μ is presented: we find g_p^μ = 8.7 ± 1.9.     

Displacive surface phases formed by hydrogen chemisorption on W {001}

A detailed LEED study is reported of the surface phases stabilised by hydrogen chemisorption on W {001}, over the temperature range 170 to 400 K, correlated with absolute determinations of surface coverages and sticking probabilities. The saturation coverage at 300 K is 19(± 3) × 10¹⁴ atoms cm^?2, corresponding to a surface stoichiometry of WH₂, and the initial sticking probability for both H₂ and D₂ is 0.60 ± 0.03, independent of substrate temperature down to 170 K. Over the range 170 to 300 K six coverage-dependent temperature-independent phases are identified, and the transition coverages determined. As with the clean surface $\text{(}\text{2}\text{×}\text{2}\text{)R45°}$ displacive phase, the c(2 × 2)-H phase is inhibited by the presence of steps and impurities over large distances (～20 Å), again strongly indicative of CDW-PLD mechanisms for the formation of the H-stabilised phases. These phases are significantly more temperature stable than the clean $\text{(}\text{2}\text{×}\text{2}\text{)R45°}$, the most stable being a c(2 × 2)-H split half-order phase which is formed at domain stoichiometries between WH_0.3 and WH_0.5. LEED symmetry analysis, the dependence of half-order intensity and half-width on coverage, and I-V spectra indicate that the c(2 × 2)-H phase is a different displacive structure from that determined by Debe and King for the clean $\text{(}\text{2}\text{×}\text{2}\text{)R45°}$. LEED I-V spectra are consistent with an expansion of the surface-bulk interlayer spacing from 1.48 to 1.51 Å as the hydrogen coverage increases to ～4 × 10¹⁴ atoms cm^?2. The transition from the split half-order to a streaked half-order phase is found to be correlated with changes in a range of other physical properties previously reported for this system. As the surface stoichiometry increases from WH to WH₂ a gradual transition occurs between a phase devoid of long-range order to well-ordered (1 × 1)-H. Displacive structures are proposed for the various phases formed, based on the hypothesis that at any coverage the most stable phase is determined by the gain in stability produced by a combination of chemical bonding to form a local surface complex and electron-phonon coupling to produce a periodic lattice distortion. The sequence of commensurate, incommensurate and disordered structures are consistent with the wealth of data now available for this system. Finally, a simple structural model is suggested for the peak-splitting observed in desorption spectra.     

Universality in the partially anisotropic three-dimensional Ising lattice

Using transfer-matrix extended phenomenological renormalization-group methods, we study the critical properties of the spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths \(\mathop J\limits^ \to = (J',J',J)\). The universality of both fundamental critical exponents y _t and y _h is confirmed. It is shown that the critical finite-size scaling amplitude ratios \(U = A_{\chi ^{(4)} } A_\kappa /A_\chi ^2 ,Y_1 = A_{\kappa ''} /A_\chi\), and \(Y_2 = A_{\kappa ^{(4)} } /A_{\chi ^{(4)} }\) are independent of the lattice anisotropy parameter Δ=J′/J. For the Y² invariant of the three-dimensional Ising universality class, we give the first quantitative estimate Y²≈2.013 (shape L×L×∞, periodic boundary conditions in both transverse directions).     

Variation of potential energy surface height and bound state depth induced by laser phase along the reaction path in atom-molecule reactions: Application to Li + CH<Subscript>4</Subscript> → LiH + CH<Subscript>3</Subscript>

Laser atom-molecule reaction interaction through polarizability and dipole moment contribution leads to potential energy surface barrier reshaping and bound states along the reaction path. The polarizability is maximum in the transition state. We will show here by using gauge representation (electric field gauge) for wave length λ = 20.6 μm, intensity I = 1 × 10¹² W/cm², I = 5 × 10¹² W/cm², I = 1 × 10¹³ W/cm², I = 3 × 10¹³ W/cm², that we can create laser induced potential energy surface barrier reshaping in the transition state region (–1–0.5 a. u.). We illustrate such effects for the LiH + CH₃ ? Li + CH₄ reaction with a barrier using ab-initio methods for calculating the reaction path, polarizability and dipole moment contribution of the atom-molecule reaction.