Monte Carlo studies of finite-size effects at first-order transitions

First-order phase transitions are ubiquitous in nature but their presence is often uncertain because of the effects which finite size has on all transitions. In this article we consider a general treatment of size effects on lattice systems with discrete degrees of freedom and which undergo a first-order transition in the thermodynamic limit. We review recent work involving studies of the distribution functions of the magnetization and energy at a first-order transition in a finite sample of size N connected to a bath of size N′. Two cases: N′ = ∞ and N′ = finite are considered. In the former (canonical ensemble) case, the distributions are approximated by a superposition of Gaussians corresponding to the different phases; all finite-size effects then vary as N or 1/N. The latter case involves the Gaussian ensemble where the entropy of the bath has a convenient form; for small N′, first-order transitions are characterized by van der Waals' loops in (for example) the energy vs. temperature curves. Results from extensive Monte Carlo simulations of Ising and Potts models in d = 2 are presented to confirm the predictions. Comparison is made with data from second-order transitions to show that the order of a transition can be distinguished through such studies, although problems still occur for first-order transitions very close to critical points.     

Supersymmetry relics in one-flavor QCD from a new 1/N expansion

We suggest a new large-N(c) limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N(c)) QCD keeping quarks in the latter. We can then define a new 1/N(c) expansion (at a fixed number of flavors N(f)) that shares appealing properties with the topological (fixed N(f)/N(c)) expansion while being more suitable for theoretical analysis. In particular, for N(f)=1, our large-N(c) limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for N(f)=1 massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.     

High-Resolution Spectrum and Rovibrational Analysis of the nu(2)/nu(5) Dyad of D(3)SiF near 700 cm(-1)

The nu(2) (A(1), 710.157 cm(-1)) and nu(5) (E, 701.717 cm(-1)) fundamental bands of D(3)(28)SiF have been studied by FTIR spectroscopy with a resolution of 2.4 x 10(-3) cm(-1). We assigned 1648 lines for the parallel band (J(max) = 50, K(max) = 21), 4279 for the perpendicular band (J(max) = 52, K(max) = 27), and in addition 671 perturbation-allowed transitions (J(max) = 50, K(max) = 12). The nearly degenerate v(2) = 1 and v(5) = 1 states are linked by (DeltaK = +/-1, Deltal = +/-1) and (DeltaK = +/-2, Deltal = -/+1) interactions, while the l(5) = +/-1 levels of nu(5) interact also by l(2, -1), l(2, 2), and l(2, -4) interactions. The first model with 36 free parameters, taking into account all these resonances through a nonlinear least-squares program, gave standard deviations of 1.56 x 10(-4) cm(-1) for 5997 nonzero-weighted IR data and 138 kHz for 8 MW data from the literature. The second model, in which the main Coriolis term was constrained to a force field value, used 37 parameters and gave similar standard deviations. A new determination of the A(0) and D(0)(K) ground state parameters was performed by two methods: either using differences between "forbidden" transitions differing by 3 in K or letting A(0) and D(0)(K) free in the global fit. The values obtained are fully compatible with those obtained previously by the "loop method." Copyright 2000 Academic Press.     

Examining coupled-channel effects in radiative charmonium transitions

Coupled-channel effects due to coupling of charmonia to the charmed and anticharmed mesons are of current interest in heavy quarkonium physics. However, the effects have not been unambiguously established. In this Letter, a clean method is proposed in order to examine the coupled-channel effects in charmonium transitions. We show that the hindered M1 radiative transitions from the 2P to 1P charmonia are suitable for this purpose. We suggest to measure one or more of the ratios Γ(h(c)'→χ(cJ)γ)/Γ(χ(cJ)'→χ(cJ)π(0)) and Γ(χ(cJ)'→h(c)γ)/Γ(χ(cJ)'→χ(cJ)π(0)), for which highly nontrivial and parameter-free predictions are given. The picture can also be tested using both unquenched and quenched lattice calculations.     

Efficiency of the microcanonical over-relaxation algorithm for vector spins analyzing first and second order transitions

We simulate vectorial spin systems solely with the microcanonical over-relaxation algorithm where the temperature is calculated by a formula of Nurdin and Schotte. We show that this procedure is the most efficient local algorithm besides the nonlocal cluster algorithm not only for first order transitions but also for second order ones. A comparison is made with the Metropolis, heat bath, multicanonical and the Creutzs demon algorithms. We study, using these algorithms, the frustrated J1-J2 model on a cubic lattice for XY, Heisenberg and O(4) spins. These models have a breakdown of symmetry Z3 SO(N)/SO(N-1) for the number N = 2,3,4 of spin components leading to transitions of first order. We show that they are strongly first order. Then, to test the over-relaxation update for second order transitions, we study a ferromagnet on a cubic lattice and a frustrated antiferromagnet on a stacked triangular lattice. We finally point out the advantages and the flaws of the over-relaxation procedure.     

Non-ergodicity transition and multiple glasses in binary mixtures: on the accuracy of the input static structure in the mode coupling theory

We examine the question of the accuracy of the static correlation functions used as input in the mode coupling theory (MCT) of non-ergodic states in binary mixtures. We first consider hard-sphere mixtures and compute the static pair structure from the Ornstein-Zernike equations with the Percus-Yevick closure and more accurate ones that use bridge functions deduced from Rosenfeld's fundamental measures functional. The corresponding MCT predictions for the non-ergodicity lines and the transitions between multiple glassy states are determined from the long-time limit of the density autocorrelation functions. We find that while the non-ergodicity transition line is not very sensitive to the input static structure, up to diameter ratios D(2)/D(1)?=?10, quantitative differences exist for the transitions between different glasses. The discrepancies with the more accurate closures become even qualitative for sufficiently asymmetric mixtures. They are correlated with the incorrect behavior of the PY structure at high size asymmetry. From the example of ultra-soft potential it is argued that this issue is of general relevance beyond the hard-sphere model.     

Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit

We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well defined when the external magnetic flux phi(e) = phi(0)/2; then the selection rules are the same as the ones for the electric-dipole transitions in usual atoms. When phi(e) does not = phi(0)/2, the symmetry of the potential of the artificial "atom" is broken, a so-called delta-type "cyclic" three-level atom is formed, where one- and two-photon processes can coexist. We study how the population of these three states can be selectively transferred by adiabatically controlling the electromagnetic field pulses. Different from lambda-type atoms, the adiabatic population transfer in our three-level delta atom can be controlled not only by the amplitudes but also by the phases of the pluses.     

Universal equations for linear adiabatic pulses and characterization of partial adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RF(max)) required for a preselected degree of inversion across a chosen effective bandwidth (bw(eff)) and for a chosen pulse length (T(p)). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bw(eff) being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bw(eff) is < or =bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, iota(bw), at the boundaries of bw(eff), two basic linear equations are found for both types of pulse and these are of the form (RF(max)T(p))(2)=m(1)T(p)bwdth+c(1) and T(p)bwdth=m(3)T(p)bw(eff)+c(3). The different behavior of the two pulses is expressed as different dependencies of the slopes m(n) and intercepts c(n) on iota(bw) and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of "linear adiabaticity." At low values of T(p)bwdth or T(p)bw(eff) the linear equations no longer apply, defining a region of "partial adiabaticity." Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RF(max) or T(p) but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RF(max) or T(p) efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of T(p)bw(eff), and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RF(max)T(p))(2) or (Total Power) T(p) versus T(p)bw(eff).     

First-order antiferro-ferromagnetic transition in Fe(49)(Rh(0.93)Pd(0.07))(51) under simultaneous application of magnetic field and external pressure

A magnetic field-pressure-temperature (H-P-T) phase diagram for first-order antiferromagnetic (AFM) to ferromagnetic (FM) transitions in Fe(49)(Rh(0.93)Pd(0.07))(51) has been constructed using resistivity measurements under simultaneous application of magnetic field (up to 8 T) and pressure (up to 20 kbar). The temperature dependence of resistivity (ρ-T) shows that the width of the transition and the extent of hysteresis decreases with pressure and increases with magnetic field. By exploiting opposing trends of dT(N)/dP and dT(N)/dH (where T(N) is the first-order transition temperature), the relative effects of temperature, magnetic field and pressure on disorder-broadened first-order transitions has been studied. For this, a set of H and P values are chosen for which T(N)(H(1),P(1)) = T(N)(H(2),P(2)). Measurements for such combinations of H and P show that the temperature dependence of resistivity is similar, i.e. the broadening (in temperature) of transition as well as the extent of hysteresis remains independent of H and P. Isothermal magnetoresistance measurements under various constant pressures show that even though the critical field required for AFM-FM transition depends on applied pressure, the extent of hysteresis as well as transition width (in magnetic field) remains constant with varying pressure.     

Measuring the transmission phase of a quantum dot in a closed interferometer

The electron transmission through a closed Aharonov-Bohm mesoscopic solid-state interferometer, with a quantum dot (QD) on one of the paths, is calculated exactly for a simple model. Although the conductance is an even function of the magnetic flux (due to Onsager's relations), in many cases one can use the measured conductance to extract both the amplitude and the phase of the "intrinsic" transmission amplitude t(D)=-i|t(D)|e(ialpha(D)) through the "bare" QD. We also propose to compare this indirect measurement with the (hitherto untested) direct relation sin((2)(alpha(D)) identical with |t(D)|(2)/max((|t(D)|(2)).     

MRI with superparamagnetic iron oxide: efficacy in the detection and characterization of focal hepatic lesions

The purpose of this study was to evaluate the potential of superparamagnetic iron oxide particles (SPIO) as tissue specific contrast agent in magnetic resonance (MR) imaging in detection and characterization of focal hepatic lesions. We investigated 45 patients with focal hepatic lesions. T1-weighted SE (TR 650/TE 15 ms) and T2-weighted SE (TR 2015-2030/TE 45 and 90 ms) unenhanced images were obtained. After SPIO application we performed T1-weighted images with and T2-weighted images with and without fat suppression using the same image parameters. Liver signal intensity decreased by 74% (min 47%, max 83%) on T2-weighted images after application of the contrast agent. Benign lesions (FNH, adenoma) showed an average signal drop of 40% (min 20%, max 47%) whereas malignant lesions showed no significant change of signal intensity on post-contrast images. The mean tumor-to-liver contrast-to-noise ratio (C/N) was improved in all post-contrast sequences irrespective of the lesion type. An additional increase of tumor-to-liver contrast by use of fat suppression technique could be established in the slightly T2-weighted sequence (TE 45 ms). In metastases, divided in different size groups, we could determine a significant size relation of tumor-to-liver C/N. After SPIO application the number of detected lesions increased distinctly, especially small foci are more easily demonstrated. SPIO particles are a efficacious contrast agent for MR examinations of the liver. For tumor characterization T1- and T2-weighted pre- and post-contrast images are necessary. The T1-weighted sequences are helpful to differentiate benign lesions such as cysts and hemangiomas from malignant lesions. Detection and differential diagnoses of hepatic lesions are improved by use of the SPIO-particles.     

Systematics of the metallization of low-Z and alkali fluids

Hydrogen, nitrogen, oxygen, cesium, and rubidium undergo nonmetal–metal (NMM) transitions in the degenerate warm fluid phase. It is quite likely that all these fluids are monatomic or very nearly so. For N, O, and H, these NMM transitions occur under quasi-isentropic compression to ～100?GPa (1?Mbar) pressures and densities of ～10 times initial liquid density in the case of H. These conditions were achieved with a two-stage gun. In the cases of Cs and Rb, these transitions occur at only ～0.01?GPa in the expanded fluid at 2000?K. These NMM transitions are Mott transitions. The values of the minimum metallic conductivities are essentially the same for all five because minimum metallic conductivity depends weakly on density of metallization and number of conduction electrons per atom. In contrast, the density dependences of the semiconductivities are very different. In the spirit of Mott, quantum mechanical wave functions of the free atoms are used to estimate the densities at which semiconductivies are appreciable. The radial extents of the charge-density distributions are well correlated with the Mott-scaled density dependences of the semiconductivities. These radial extents depend on the degree to which the filled-electron core screens the valence electron(s) from the nuclear Coulomb force. This simple picture gives a qualitative explanation for the density dependences of the semiconductivities of all five and for the Herzfeld criterion, which predates quantum mechanics.     

Probing the superconducting gap symmetry of PrOs4Sb12: a penetration depth study

We report measurements of the magnetic penetration depth lambda in single crystals of PrOs4Sb12 down to 0.1 K, with the ac field applied along the a, b, and c directions. In all three field orientations, lambda approximately T2 and superfluid density rho(s) approximately T2 for T<0.3T(c). Data are best fit by the 3He A-phase-like gap with multidomains, each having two point nodes along a cube axis, and parameter Delta(0)(0)/k(B)T(c)=2.6, suggesting that PrOs4Sb12 is a strong-coupling superconductor with two point nodes on the Fermi surface. We also confirm the double transitions at 1.75 and 1.85 K seen in other measurements.     

Entropic rigidity of randomly diluted two- and three-dimensional networks

In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.     

Anisotropies of the lower and upper critical fields in MgB2 single crystals

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.     

Chemical memory erasure; a photochemical model

In this paper we propose an exactly solvable model of a topological insulator defined on a spin- \(\tfrac{1}{2}\) square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin- \(\tfrac{1}{2}\) Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model’s ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem’s spectrum from band to flat-band states.     

QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

Physical properties and crystal chemistry of Ce2Ga12Pt

Single crystals of the new ternary compound Ce(2)Ga(12)Pt were prepared by the self-flux technique. The crystal structure with the space group P4/nbm was established from single crystal x-ray diffraction data and presents a derivative of the LaGa(6)Ni(0.6) prototype. Magnetic susceptibility measurements show Curie-Weiss behaviour due to local Ce(3+) moments. At high temperatures, the magnetic anisotropy is dominated by the crystal-electric-field (CEF) effect with the easy axis along the crystallographic c direction. Ce(2)Ga(12)Pt undergoes two antiferromagnetic phase transitions at T(N,1) = 7.3 K and T(N,2) = 5.5 K and presents several metamagnetic transitions for the magnetic field along c. Specific-heat measurements prove the bulk nature of these magnetic transitions and reveal a doublet CEF ground state. The 4f contribution to the resistivity shows a broad maximum at T(max) ≈ 85 K due to Kondo scattering off the CEF ground state and excited levels.     

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

We study the ground-state phase diagram of the frustrated spin-[Formula: see text] antiferromagnet with J(2) = xJ(1) > 0 (J(1) > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x(c(1)) < x < x(c(2)), where x(c(1)) ≈ 0.207 ± 0.003 and x(c(2)) ≈ 0.385 ± 0.010. The transition at x(c(1)) to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ? x ? 0.24), while that at x(c(2)) is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point [Formula: see text]. The spiral phases that are present classically for all values x > 1/6 are absent for all x ? 1.     

Exact universal amplitude ratios for two-dimensional Ising models and a quantum spin chain

Let f(N) and xi(-1)(N) represent, respectively, the free energy per spin and the inverse spin-spin correlation length of the critical Ising model on a N x infinity lattice, with f(N)-->f(infinity) as N-->infinity. We obtain analytic expressions for a(k) and b(k) in the expansions N( f(N)-f(infinity)) = SUM (k = 1)(infinity)a(k)/N(2k-1) and xi(-1)(N) = SUM (k = 1)(infinity)b(k)/N(2k-1) for square, honeycomb, and plane-triangular lattices, and find that b(k)/a(k) = (2(2k)-1)/(2(2k-1)-1) for all of these lattices, i.e., the amplitude ratio b(k)/a(k) is universal. We also obtain similar results for a critical quantum spin chain and find that such results could be understood from a perturbated conformal field theory.