Magnetic correlations in three-dimensional ising spin glasses

By a recursive method numerically exact free energies are calculated forL×L×M Ising lattices with random bonds andL=4, 4M10, applying free boundaries in the direction where the lattice is less small and otherwise periodic boundary conditions. Both for the±J model and the gaussian model the specific heat is in fair agreement with Monte Carlo results obtained for much larger lattices. However, the correlation function [S ₀ S _{R T} ² ]_av is found to decay exponentially with distanceR [for 1R9] at temperatures far below the apparent freezing temperatures of the Monte Carlo simulations, implying that there is no nonzero Edwards-Anderson order parameter in equilibrium. This behavior is qualitatively different from Mattis spin glasses (or Ising ferromagnets) where even smaller lattices show pronounced magnetic order at low temperatures. As the Monte Carlo results give evidence for a nonzero Edwards-Anderson order parameter (for not too long observation times), which is fairly independent of lattice size down to sizes of 4³, we suggest that Edwards-Anderson ordering is a nonequilibrium phenomenon visible only in studying dynamic properties.     

Finite size scaling analysis of ising model block distribution functions

The distribution functionP _L (s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [P _L ^(f) (s)] and periodic [P _L ^(p)(s) ] boundary conditions is treated. Above the critical pointT _c , these distributions tend for largeL towards the same gaussian distribution centered around zero block magnetization, while belowT _c these distributions tend towards two gaussians centered at ±M, whereM is the spontaneous magnetization appearing in the infinite systems. However, belowT _c the wings of the distribution at small |s| are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases.At criticality, the distribution functions tend for largeL towards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained.As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions:(i) standard estimates of order parameter, susceptibility, interface tension are improved(ii) T _c can be estimated independent of critical exponent estimates(iii) A Monte Carlo renormalization group similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort(iv) Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.     

Surface structure for three-dimensional percolation clusters abovep c

We study the surface behaviour of very large percolation clusters above the critical concentrationp _c by considering the width and the analogue of surface tension of the interface separating the interior of the cluster from the outside region. Our Monte Carlo simulation techniques, which are described in detail, are applied to a quadraticL ×L surface layer on the simple cubic lattice, withL up to 200. They give clearly a rough surface even for the highest concentrationsp. The data forp=1 suggest a logarithmic divergence for the interface width in the thermodynamic limitL.     

Stability of 3He2 4He M and 3He3 4He M L = 0,1 Clusters

We have studied the stability of mixed ³He/⁴He clusters in L = 0 and L = 1 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu (TTY) He-He potential. The clusters ³He⁴He_M ( ) and ³He₂⁴He_M (L = 0, S = 0) are stable for M > 1, while to bind two ³He in a triplet state the minimum number of ⁴He is four. Considering clusters with three ³He, ³He₃⁴He₄ is the smallest stable system in the L = 1 state, while ³He₃⁴He₈ is the smallest stable system in the L = 0 state.     

Critical behavior of the site percolation model on the square lattice in aL×M geometry

Relevant aspects of the critical behavior of the site percolation model in aL×M geometry (LM) are studied. It is shown that this geometry favors the growth of percolating clusters in theL-direction with respect to those growing in theM-direction, causing pronounced finite-size effects on the percolation probabilities. Scaling functions have an additional parameter, namelyM, which introduces a dependence of these functions on the aspect ratioL/M. At criticality, the probability of a site belonging to the percolation clusters (P _L,M ) behaves likeP _L,M L ^/v (L/M) with =5/36 andv=4/3, where is a suitable scaling function. Using scaling arguments it is conjectured and then tested by means of Monte Carlo simulations, the following asymptotic behavior (L/M)(L/M), (L,M, =1), for the leading term. Systematic deviations of the Monte Carlo data from the conjectured behavior are due to second order corrections to the leading term which can also be under-stood on the basis of scaling ideas. Finite-size dependent critical probabilities are also functions ofL/M as it follows from scaling arguments which are corroborated by the simulations.Financially supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) de la República Argentina     

Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice

A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the lattice. The stiffness exponent governing the scaling of the defect energy E with system size L, (E) ~L ^y, is obtained as y ₃ = 0.25546(3) by reducing the equivalent of lattices up to L = 2¹⁰⁰ in d = 3, and as y ₄ = 0.76382(4) for up to L = 2³⁵ in d = 4. The reduction rules allow the exact determination of the ground state energy, entropy, and also provide an approximation to the overlap distribution. With these methods, some well-know and some new features of diluted hierarchical lattices are calculated.     

Universality class of interface growth with reflection symmetry

We investigate interface dynamics in 1+1 dimensions, respecting reflection symmetry. In the continuum approach of Kardar, Parisi, and Zhang, the leading nonlinearity is then of the form (h _t)³. On the basis of Monte Carlo simulations for a driven lattice gas, we argue that the nonlinearity is marginally irrelevant. Thus, the universality class is the one of equilibrium interfaces with a purely relaxational bulk dynamics.     

Molecular dynamics calculation for the modified xy model

In order to demonstrate the effectiveness of molecular dynamics (MD) for the determination of the density of states of a system that suffers an abrupt change of state, we have performed extensive calculations for the modified rotor model, defined by the interaction potentialV() = 2J{1 – [cos(/2)] ^{p 2}} between neighboring rotors. Our results for 2-dimensionalL×L lattices withL=8, 16, 32, and 64 demonstrate clearly that the transition is continuous forp ²24, but suggest a first-order transition forp ²28.     

Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f ₀(980), a ₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η ₈ mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p ⁴) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m _s/ , in terms of the O(p ⁴) CHPT low-energy constant combinations 2L ^r ₈ - L ^r ₅ and 2L ^r ₆ - L ^r ₄. In this way, we give a range for the values of these low-energy counterterms and for 3L ₇ + L ^r ₈, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m _s/ = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.     

Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Critical behavior of the specific heat for pure and site-diluted simple cubic Ising systems

The exponent of the specific heatC is determined for the pure and the site-diluted simple cubic Ising model (concentrationx=0, 0.2, 0.4 of nonmagnetic sites) by a finite-size scaling analysis of the peak value C_max(L) for systems of linear dimensionsL=8, 16, 32, and 64. The C_max values are obtained by the Ferrenberg-Swendsen algorithm, using Monte Carlo data from a fully-vectorized multi-spin coding program. We obtain =0.11 for x=0 and a crossover to a negative value upon dilution, with =–0.029(4) both forx=0.2 andx=0.4.     

Non-perturbative study of the light pseudoscalar masses in chiral dynamics

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S -wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈ . The former are found to dominate the physical pseudoscalar masses. We also match our results with the self-energies from Chiral Perturbation Theory (CHPT) to O(p ⁴) , and resum higher orders from our calculated self-energies. A robust relation between several O(p ⁴) CHPT counterterms is then obtained. By taking into account values determined from previous chiral phenomenological studies of m _s/ and 3L ₇ + L ^r ₈(M _ρ) , we determine a tighter region of favoured values for the O(p ⁴) CHPT counterterms 2L ^r ₆(M _ρ) - L ^r ₄(M _ρ) and 2L ^r ₈(M _ρ) - L ^r ₅(M _ρ) . This determination perfectly overlaps with the recent determinations to O(p ⁶) in CHPT. We warn about a likely reduction in the value of m _s/ by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m _s/ and 3L ₇ + L ^r ₈(M _ρ) .     

Domain-wall energy in sintered Nd15Fe77B8 permanent magnet

From measurements of the magnetic domain widthsD versus grain thicknessL, we have determined the domain wall energy in the demagnetized state for a sintered Nd₁₅Fe₇₇B₈ magnet: = 56 erg/cm². Using this wall energy and the published magnetocry-stalline constantK ₁=4.9×10⁷ erg/cm³, we have calculated the exchange constantA=4.0×10^–6 erg/cm, domain wall thickness _B=89 Å, and the critical diameter for single domain particlesD _c=0.67 m.     

Nonperturbative equation of state of quark-gluon plasma: Applications

The vacuum-driven nonperturbative factors L_i for quark and gluon Green’s functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for μ = 0 including P/T⁴, ε/T⁴, . The basic role in the dynamics at T ? 3T_c is played by the factors L_i which are approximately equal to the modulus of Polyakov line for quark L_fund and gluon L_adj. The properties of L_i are derived from field correlators and compared to lattice data, in particular the Casimir scaling property follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for P/T⁴, ε/T⁴, are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.     

Universal crossing probabilities and incipient spanning clusters in directed percolation

Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio r _eff = ct/L ^z, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture. Received 10 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: turban@lpm.u-nancy.fr RID="b" ID="b"UMR CNRS 7556     

On estimating the top quark mass from global analyses ofe + e − collision data

A study is undertaken to determine how to best extract the top quark massm _t within the Minimal Standard Model (MSM) using a global fit to a variety of processes (including wide-angle Bhabha scattering) ine ⁺ e ^– collisions near theZ which should be measured in the coming years. Experimental cuts are accommodated as an integral part of the analysis. It is advantageous to use the collinear radiation approximation and to cut data in rapidity, center-of-mass polar angle and minimum final state invariant mass squared,s. This avoids the need for the largest Monte Carlo acceptance correction to the data. Further, high precision cross section, calculations, (which include all one-loop electroweak and QED effects, certain higher-order improvements and perturbative QCD corrections as well as exponentiated soft and collinear photon radiation) then no longer require a Monte Carlo. This results in a speedup factor of at least fifty thousand (>5×10⁴) in EXPOSTAR. The data (corrected only for detector cracks, resolution and small non-collinear radiation effects) can therefore be fit quickly and directly forM _z ,m _t ,m _Higgs and _strong without recourse to unphysical intermediate quantities (weak mixing angles, running couplings, partial widths, ^*, etc.) Determination ofm _t could be as precise as ±15 GeV (and another±20 GeV fromm _Higgs) at the end of LEP running in 1991. Longitudinally polarized beams with very small polarization error could give an error onm _t smaller, by a factor 4 for the same luminosity.     

The Ising square lattice in aL×M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers

Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthML, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a terrace of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary fields is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the boundary). Extensive Monte Carlo calculations on this model performed on a multi-transputer system are presented and analyzed in terms of phenomenological finite size scaling concepts. The fact that two scaling variables occur (/L,L/M, with being the correlation length in the bulk) is demonstrated explicitly. In the absence of boundary fields, the system forML orders nearT _c in a domain state, with domain walls running across the terrace, while at some temperature belowT _c a transition to a monodomain state occurs. This domain state slightly belowT _c is suppressed, however, by rather weak boundary fields. These results are interpreted in terms of exact theoretical predictions.