Langevin Simulation of the Chirally Decomposed Sine-Gordon Model

A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing with these models, alternative computational strategies have been proposed along the years. The Langevin technique, in particular, is known to be frequently plagued with difficulties such as strong numerical instabilities or subtle ergodic behavior. Regarding the chirally decomposed version of the sine-Gordon model as a prototypical case for the failure of the Langevin approach, we devise a truncation prescription in the stochastic differential equations which yields numerical stability and is assumed not to spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is supported by a finite size scaling analysis, whereby a massive phase ending at a line of critical points is clearly observed for the truncated stochastic model.Comment: 6 pages, 4 figure

Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

Amorphous-amorphous transition and the two-step replica symmetry breaking phase

The nature of polyamorphism and amorphous-to-amorphous transition is investigated by means of an exactly solvable model with quenched disorder, the spherical s+p multi-spin interaction model. The analysis is carried out in the framework of Replica Symmetry Breaking theory and leads to the identification of low temperature glass phases of different kinds. Besides the usual `one-step' solution, known to reproduce all basic properties of structural glasses, also a physically consistent `two-step' solution arises. More complicated phases are found as well, as temperature is further decreased, expressing a complex variety of metastable states structures for amorphous systems.Comment: 8 pages, 7 figures, longer version, new references adde

An approach to NLO QCD analysis of the semi-inclusive DIS data with modified Jacobi polynomial expansion method

It is proposed the modification of the Jacobi polynomial expansion method (MJEM) which is based on the application of the truncated moments instead of the full ones. This allows to reconstruct with a high precision the local quark helicity distributions even for the narrow accessible for measurement Bjorken $x$ region using as an input only four first moments extracted from the data in NLO QCD. It is also proposed the variational (extrapolation) procedure allowing to reconstruct the distributions outside the accessible Bjorken $x$ region using the distributions obtained with MJEM in the accessible region. The numerical calculations encourage one that the proposed variational (extrapolation) procedure could be applied to estimate the full first (especially important) quark moments

On the Phase Structure of the 3D Edwards Anderson Spin Glass

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses.Comment: 30 pages and 17 figures. Final version to be published in PR

Multiplicative Noise: Applications in Cosmology and Field Theory

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure

Renormalization Group Running of Newton's G: The Static Isotropic Case

Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equations, intended to incorporate the full scale dependence of $G$, and examined in the case of the static isotropic metric. The existence of vacuum solutions to the effective field equations in general severely restricts the possible values of the scaling exponent $\nu$.Comment: 61 pages, 3 figure

Lattice simulations of real-time quantum fields

We investigate lattice simulations of scalar and nonabelian gauge fields in Minkowski space-time. For SU(2) gauge-theory expectation values of link variables in 3+1 dimensions are constructed by a stochastic process in an additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and the use of a tilted real-time contour leads to converging results in general. All fixed point solutions are shown to fulfil the infinite hierarchy of Dyson-Schwinger identities, however, they are not unique without further constraints. For the nonabelian gauge theory the thermal equilibrium fixed point is only approached at intermediate Langevin-times. It becomes more stable if the complex time path is deformed towards Euclidean space-time. We analyze this behavior further using the real-time evolution of a quantum anharmonic oscillator, which is alternatively solved by diagonalizing its Hamiltonian. Without further optimization stochastic quantization can give accurate descriptions if the real-time extend of the lattice is small on the scale of the inverse temperature.Comment: 36 pages, 15 figures, Late

Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure